piv study of fractal grid turbulence
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PIV study of fractal grid turbulence
S. Discetti1, I. B. Ziskin2, R.J. Adrian2, K. Prestridge3
1DIAS, University of Naples Federico II, Naples (Italy)2School for Engineering of Matter, Transport and Energy,
Arizona State University, AZ (USA)3Los Alamos National Laboratory, NM (USA)
2nd UK-JAPAN Bilateral and 1st ERCOFTAC Workshop, Imperial College London
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Motivation
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
Square space-filling fractal grids 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
Experimental setup
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
Experimental setup
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.
385mm
600mm
Measurement area
≈50mm
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Particle Image Velocimetry
p
p
o y
x
tMvu 1
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 250 m μ
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.
Test procedure
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Mean flow features
U [m/s] U [m/s] U [m/s]
Mean streamwise velocity for tr=13 and ReM=3.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Mean flow features
Mean streamwise velocity for tr=13 and ReM=3.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Turbulent fluctuations
tr =13ReM =3.5∙103
u2 [m2/s2]
v2 [m2/s2]
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Anisotropy of the Reynolds tensor
tr =13ReM =3.5∙103
u2/ v2
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Two-point correlation
tr =13ReM =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
Longitudinal and transverse correlation functions
xurxurR 1111
tr =13ReM =3.5∙103
x/x*=0.47
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
Longitudinal and transverse correlation functions
xurxurR 2222
tr =13ReM =3.5∙103
x/x*=0.47
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
2nd order structure functions
21111 xurxurD
tr =13ReM =3.5∙103
x/x*=0.47
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
2nd order structure functions
tr =13ReM =3.5∙103
x/x*=0.47
This is not equivalent to the transverse 2nd order structure function (the velocity component is always the crosswise one).
22222 xurxurD
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Turbulent kinetic energy decay
Space filling square fractal grids are characterized by an unusually fast decay: is it governed by an exponential law or a power law?
CBxu 2 CBx
eu
2
tr =13 ReM =11.5∙103
B=0.526 C=0.262R2=0.91
B=-0.481 C=-3.90R2=0.91
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Turbulence decay
CBx
eu
2
Exponential decay
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
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
ReM =3.5∙103
ReM =11.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Turbulence decay
ReM =3.5∙103
ReM =11.5∙103 CBxu 2
Power-law decay
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
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
Turbulence decay
CBx
eu
2ReM =11.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Turbulence decay
CBxu 2ReM =11.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Turbulence decay - remarks
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
Single lengthscale turbulence decay
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
Single lengthscale turbulence decay
tr = 13 X = 385 mm
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Taylor lengthscale measurement
DIRECT METHOD: 2
2
xu
uT
INDIRECT METHOD:
211
2
2
xR
uT
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Taylor lengthscale measurement
DIRECT METHOD:
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.
2
2
xu
uT
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Taylor lengthscale measurement
INDIRECT METHOD:
211
2
2
xR
uT
The peak of the two-point correlation is fitted with a parabolic function:
2
22
11 21
T
rurR
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Taylor lengthscale measurement
INDIRECT METHOD:
211
2
2
xR
uT
The peak of the two-point correlation is fitted with a parabolic function:
2
22
11 21
T
rurR
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Taylor lengthscale measurement
INDIRECT METHOD:
211
2
2
xR
uT
According to Adrian and Westerweel (2011):
21111
~ rRrRE Idr ,
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Taylor lengthscale measurement
INDIRECT METHOD:
211
2
2
xR
uT
According to Adrian and Westerweel (2011):
21111
~ rRrRE Idr ,
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
Taylor lengthscale measurement
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.
INDIRECT METHOD:
211
2
2
xR
uT
2
2
211
2
0~u
uRuSNR
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Taylor lengthscale measurement
2
2
211
2
0~u
uRuSNR
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Taylor lengthscale measurement
Direct method Indirect method
tr =13 ReM =3.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Taylor lengthscale measurement
tr =13 ReM =3.5∙103 tr =13 ReM =11.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Dissipation rate
DIRECT METHOD:
ENERGY BALANCE:
212
222
211 123 SSS
xqU
2
21
One can use the relations of the power law and exponential decay.
INDIRECT METHOD: 2
2
15T
u
One can use the Taylor lengthscale estimated with the indirect method.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Dissipation rate
tr =13
ReM =3.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Conclusion
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.).
Thank you for your attention
ACKNOWLEDGMENTS
This research was supported in part by Contract 79419-001-09, Los Alamos National Laboratory.
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