PIV Measurements of Flow Structure and Turbulence within and above a Corn Canopy and a Wind ...

164 Pages·2008·14.91 MB·English

PIV Measurements of Flow Structure and Turbulence within and above
a Corn Canopy and a Wind Tunnel Model Canopy

by
Weihong Zhu

A dissertation submitted to The Johns Hopkins University in conformity with the
requirements for the degree of Doctor of Philosophy

Baltimore, Maryland
May, 2006

 Weihong Zhu 2006
All rights reserved
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Abstract
Particle Image Velocimetry (PIV) measurements just within and above a mature
corn canopy have been performed to clarify the small-scale spatial structure of the
turbulence. Frequency spectra are combined with instantaneous spatial spectra to resolve
more than five orders of magnitudes of length scales which display an inertial range
spanning three decades. The small scale turbulence in the dissipation range exhibits
anisotropy at all measurement heights. Directly calculated subgrid scale (SGS) energy
flux increases significantly with decreasing filter size, providing support for existence of
spectral shortcut that bypasses the cascading process. As a result, the cascading energy
flux is overestimated by a -5/3 line fit to the spectra, but not by orders of magnitude.
Quadrant-Hole (Q-H) analysis shows that small scale flow structures that dominate the
vorticity and cascading dissipation rate, and large scale structures that dominate the
Reynolds stresses and production rate seem to have very little correlation with each other.
However sweep events are the largest contributors to both at least close to canopy height.
Although the outward interaction events are rare, they are highly dissipative and
significantly contribute to the overall dissipation and (negative) production rates.
Turbulence characteristics measured in the filed are compared with those of a
model canopy setup in a wind tunnel. The laboratory normalized mean velocity profile is
adjusted using variable mesh screens to match the normalized mean shear of the corn
field data. However the profiles of normalized Reynolds shear stress in the field and the
laboratory differ. A comparison of results from Q-H analysis for both data sets shows that
in quadrants 1 to 3, the wind tunnel and field conditionally sampled stresses show similar
trends. However, a conflicting trend is found in the sweep quadrant, presumable due to
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the difference in roughness density. The analysis confirms that sweeps and ejections
dominate the momentum flux and dissipation rate.
Furthermore, quadrant analysis of the wind tunnel data reveals fundamental
differences in flow structure, especially between sweep and ejection events, which
dominate the flow in terms of duration. The differences in flow structure affect the
distributions of turbulent kinetic energy (TKE), Reynolds shear stress, turbulence
production, turbulent diffusion, and dissipation rates. During sweeps the TKE and
Reynolds shear stress have distinct peaks just below canopy height, whereas during
ejections they have broad maxima well above the canopy. A distinct large peak in
production just below canopy height during sweep events is the main contributor to the
high overall production there. At z/h > 1.2, ejections take over. Since eddies generated
within the wakes behind canopy elements are already within the dissipation range, the
extent of dissipation below canopy height increases with velocity magnitude.
Consequently, the dissipation there has the highest values during sweep and quadrant 1
events, and is significantly lower during ejection and quadrant 3 events. Well above the
canopy, ejections are the most dissipative. Turbulent diffusion during sweep events acts
as source below narrow shear layer within the canopy and a sink above it. Diffusion
during ejection events is a source only well above the canopy.

Advisor: Prof. Joseph Katz
Readers: Prof. Charles Meneveau, Prof. Thomas Osborn
iii
Acknowledgements

I would like to acknowledge many people who made this dissertation possible.
First, I would like to express my deepest gratitude to my advisor, Prof. Joseph Katz for
offering me this challenging research opportunity and his continuous support. Without his
insightful guidance and sound advice throughout this research process, I would never
have been able to finish this dissertation.
Second, I would like to thank my readers, Prof. Thomas Osborn and Charles
Meneveau for taking the time to review my dissertation and for their insightful comments
and suggestions. I am very grateful towards Prof. Thomas Osborn for giving me the
opportunity to take part in the ocean project which is led by him and Prof. Joseph Katz. I
would like to thank Prof. Meneveau for some very valuable discussions on subgrid scale
energy flux calculation. Also I thank him and his research group for assistance and
support during our wind tunnel experiment.
I am also very grateful to Dr. Rene van Hout, one of the key persons to the
success of this project. His efforts in field and wind tunnel experiment, and many
discussions are highly appreciated. My thanks are due also to Dr. Wusi Yue for
discussions on applying experiment data to numerical simulation. I would also like to
express my gratitude to Dr. Hyung-Suk Kang for providing hotwire anemometer data in
the wind tunnel experiment, and to Dr. Jan Kleissl and Prof. Marc Parlange for the sonic
anemometer data in the field. I thank Mike Embry of the Wye Research and Education
Center of the University of Maryland for his help in finding us a proper corn field, and
Mac Farms Inc. in Hurlock, MD, for granting us access to their corn field.
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Special thanks are due to Dr. Yury Ronzhes and Mr. Stephan King for their
technical support in the field and lab. I would like to thank Dr. Luksa Luznik for the
invaluable discussion in data analysis and his help in the corn field experiment. Also I
wish to thank many students and post-doctoral fellows in our lab for forming such a
supportive team.
This dissertation is dedicated to my wife Xiuping Wang, our parents, daughter
Jessica, and son Richard for their supports, sacrifices, and our loss of precious time
together.
This work was funded by Bio-Complexity Program of the National Science
Foundation.
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Table of Contents
Page
Abstract ii
Acknowledgements iv
Table of Contents vi
List of Tables ix
List of Figures x
Chapter 1 Introduction 1
Chapter 2 PIV measurements within and above a mature
corn canopy: Statistics and energy flux 7
2.1 Description of the field experiments 8
2.1.1 Setup and conditions 8
2.1.2 Corn field characteristics 11
2.2 Experimental results 12
2.2.1 Mean flow characteristics 12
2.2.2 Spectral characteristics and cascading energy flux 15
2.2.3 SGS energy flux 23
2.2.4 Terms appearing in the turbulent kinetic energy budget 25
2.2.5 The relation between the dissipation rate and the out of plane
component of the vorticity 27
Chapter 3 Quadrant-Hole analysis of canopy turbulence in the corn field 48
3.1 Definition of parameters 49
vi
3.2 Conditional sampling of Reynolds shear stress and vorticity magnitude 51
3.3 Conditional sampling of dissipation rate 54
3.4 Conditional sampling of production 59
Chapter 4 A comparison of canopy turbulence in the field and
in a wind tunnel model 74
4.1 Wind tunnel experiment setup 75
4.2 Mean and turbulent statistics 77
4.3 Spectral characteristics 79
4.4 Quadrant-Hole analysis 82
Chapter 5 Flow structure and conditionally averaged mean
and turbulence profiles in the wind tunnel model canopy 94
5.1 Flow structure of ejection and sweep events at canopy height 95
5.2 Conditional averaging of mean flow, TKE and shear stress 96
5.2.1 Duration and mean profiles 96
5.2.2 Conditionally averaged TKE and Reynolds stress 98
5.3 Spectra, length scales, TKE and shear stress budget 100
5.3.1 Spectra, energy flux and length scales 100
5.3.2 Conditional sampling of TKE and shear stress budget 106
Chapter 6 Summery and conclusion 131
6.1 A summary of corn field measurements 131
6.2 Wind tunnel measurements and a comparison with field data 135
vii
6.3 Discussion 139
Literature 142
Curriculum Vita 150
viii
List of Tables
Page
Table 2.1 Comparison of the mean flow and turbulence parameters
between Sonic Anemometers (CSAT) and Particle Image
Velocimetry (PIV). 30
Table 2.2 Mean friction velocities and mean velocities at canopy
height (h = 2.67m) used for normalizing the PIV data. 30
Table 2.3 Turbulence parameters calculated from the PIV data. 31
Table 2.4 Convective transport of kinetic energy terms (I) normalized
by u3/h. 31
*
Table 2.5 Production terms (V) normalized by u3/h. 32
*
Table 2.6 Turbulent diffusion terms (III) normalized by u3/h. 32
*
Table 4.1 Mesh size of the shear generator. 85
Table 4.2 Comparison of dissipation rate estimated by direct calculation,
ε (Eq. 4.1), and by a -5/3 line fit to the energy spectra, ε for
d
wind tunnel data. 86
Table 5.1 The Kolmogorov scale corresponding to ε and ε, Taylor scale,
d
Taylor scale Reynolds number, integral scale and a comparison
of dissipation rates estimated by a −5/3 line fit to the energy
spectra, ε, to direct calculation, ε, and to SGS energy flux,
d
ε , at ∆~70η. 114
SGS
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List of Figures
Page
Fig. 2.1 Schematic layout of the instruments during the field experiment.
(not to scale)
PIV system Meteorological station 33
Fig. 2.2 Schematic layout of the platform carrying the PIV system
and the relative position of the camera and the light sheet.
(not to scale) 34
Fig. 2.3 Typical vector map of the instantaneous velocity field
superimposed on the vorticity distribution. The instantaneous
spatial mean velocity is subtracted to highlight the flow structure. 35
Fig. 2.4 Calculation of the Leaf Area Index and Projected Frontal Area
Index of corn plants. 36
Fig 2.5 Five minute averaged wind velocities and wind directions on
22 July 2003. Error bars indicate standard deviation.
PIV CSAT RMY (z/h = 1.5)
z/h = 0.97 z/h = 1.0 Wind speed
z/h = 1.11 z/h = 1.35 Wind direction
z/h = 1.20
z/h = 1.29 37
Fig. 2.6 Mean flow and turbulence statistics of the corn canopy flow. 38
Fig. 2.7 Comparison of one-dimensional energy spectra obtained from
PIV (time series and spatial at z/h = 0.97) and CSAT (z/h = 1.0). 39
Fig. 2.8 Normalized longitudinal spectra of PIV data at different heights. 40
x