FUSION OF NUMERICAL MODELING AND INNOVATIVE SENSING
TO ADVANCE BRIDGE SCOUR RESEARCH AND PRACTICE
by
JUNLIANG TAO
Submitted in partial fulfillment of the requirements
For the degree of Doctor of Philosophy
Dissertation Advisor: Dr. Xiong (Bill) Yu
Department of Civil Engineering
CASE WESTERN RESERVE UNIVERSITY
August, 2013 CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the thesis/dissertation of
Junliang Tao
candidate of Doctor of Philosophy degree*
Xiong (Bill) Yu
(Committee Chair) Xiangwu (David) Zeng
Adel S. Saada
Jaikrishnan R. Kadambi
Chung-Chiun Liu
(date) 06/14/2013
* We also certify that written approval has been obtained for any proprietary material contained therein.
DEDICATION
To Baba, Mama and Liangliang
TABLE OF CONTENTS
List of Tables ...... vii
List of Figures ...... viii
Acknowledgement ...... xv
List of Abbreviations ...... xvii
Abstract ...... xx
Chapter 1 Introduction ...... - 1 -
1.1. Background ...... - 1 -
1.2. Bridge Scour Basics ...... - 2 -
1.2.1. Definition and Components ...... - 2 -
1.2.2 Typical turbulence structures around a circular cylinder ...... - 4 -
1.2.3. Erosion and Sediment transport ...... - 7 -
1.2.4. Scour hole development ...... - 12 -
1.3. Research Objectives ...... - 14 -
1.4. Organization of the dissertation ...... - 15 -
Chapter 2 A Synthetic review on CFD modeling of bridge scour ...... - 19 -
2.1 Single-phase models for bridge scour modeling ...... - 21 -
2.1.1. Reynolds Averaged Navier-Stokes (RANS) models ...... - 23 -
2.1.2. Large Eddy Simulation (LES) models ...... - 30 -
i
2.1.3. Detached Eddies Simulation (DES) models ...... - 34 -
2.2 Two-phase models for bridge scour modeling...... - 40 -
2.2.1. Eulerian-Eulerian coupling models...... - 41 -
2.2.2. Eulerian-Lagrangian Models ...... - 42 -
2.2.3. Lagrangian-Lagrangian Models ...... - 44 -
2.3. Discussions ...... - 46 -
2.3.1. Comparison of different turbulence modeling strategies ...... - 46 -
2.3.2. Methods for discretization and gridding ...... - 49 -
2.3.3. Treatment of Boundary conditions ...... - 52 -
2.3.4. Modeling of sediment transport and erosion ...... - 53 -
2.4. Summary and Conclusions ...... - 57 -
Chapter 3 CFD modeling of effects of pier configurations
on the flow pattern and scour ...... - 59 -
3.1. Introduction ...... - 59 -
3.2. Numerical methods and verification ...... - 62 -
3.3. Simulation cases and computational details ...... - 70 -
3.4. Effect of Pier Shape ...... - 72 -
3.4.1. Vortex structure ...... - 72 -
3.4.2 Vertical velocity ...... - 74 -
3.4.3 Shear stress...... - 75 -
ii
3.4.4 Scour pattern ...... - 76 -
3.5. Effect of aspect ratio ...... - 78 -
3.5.1. Vortex structure ...... - 78 -
3.5.2 Vertical velocity ...... - 79 -
3.5.3 Shear Stress ...... - 80 -
3.5.4 Scour pattern ...... - 81 -
3.6. Effect of attack angle ...... - 83 -
3.6.1 Flow pattern ...... - 84 -
3.6.2. Shear stress...... - 84 -
3.6.3. Scour pattern ...... - 88 -
3.7. Implication to scour mechanism and practical significance ...... - 89 -
3.8. Recommendations toward modeling of the scour process ...... - 92 -
3.8.1. The framework ...... - 92 -
3.8.2. An in-depth view on the bed load formulas ...... - 99 -
3.8.3. Modification on the critical shear stress ...... - 103 -
3.8.4. Alternative modification method for the bed load transport equations .... - 106 -
3.9. Summary and conclusions ...... - 107 -
Chapter 4 From Bio-inspiration to Bio-mimicking:
A multidisciplinary review on hair flow sensor ...... - 110 -
4.1. Introduction ...... - 110 -
iii
4.2. Bio-inspiration: Lateral line system of aquatics ...... - 111 -
4.2.1. Number and distribution of Canal Neuromasts (CNs)
and Superficial Neuromasts (SNs) ...... - 112 -
4.2.2. Directional sensitivity ...... - 113 -
4.2.3. Flow sensing mechanism: experimental discoveries and biomechanical
sensing model...... - 114 -
4.3. Bio-mimicking: Artificial hair flow sensors ...... - 128 -
4.3.1 Piezoresistive BHFS ...... - 129 -
4.3.2 Capacitive BHFS ...... - 138 -
4.3.3 BHFS based on other principles ...... - 143 -
4.4. On the Methods for Information Processing ...... - 144 -
4.5 Summary ...... - 149 -
Chapter 5 Innovative bio-inspired hair sensors based on Piezoelectric microfibers .. - 150 -
5.1. Introduction ...... - 150 -
5.2. Piezoelectric microfiber based hair sensor with surface electrodes ...... - 151 -
5.2.1. Sensor design and computer modeling-assisted performance analysis .... - 151 -
5.2.2. Sensor fabrication and validation of its directional response ...... - 160 -
5.3. Piezoelectric microfiber based hair sensor with spiral electrodes ...... - 165 -
5.3.1. Sensing principle and sensor design ...... - 165 -
5.3.2. Modeling of the sensing mechanisms ...... - 167 -
iv
5.3.3. Prototype fabrication and evaluation ...... - 173 -
5.3.4. Application of the proposed sensor as a flow sensor inspired
by the lateral line ...... - 180 -
5.4. Piezoelectric microfiber based hair sensor with artificial cupula ...... - 181 -
5.4.1. Inspiration and sensor design ...... - 181 -
5.4.2. Modeling and optimization ...... - 182 -
5.5. Influence of Shunt-damping circuit on the dynamic
response of the bio-inspired sensor ...... - 192 -
5.5.1. Theoretical basis and implementation in COMSOL® ...... - 193 -
5.5.2. The influence of the external circuit on the frequency
response of the sensor ...... - 196 -
5.5.2. Comparisons and discussions ...... - 203 -
5.6. Summary and Conclusions ...... - 205 -
Chapter 6 A TDR Field Bridge Scour Monitoring System...... - 208 -
6.1. Introduction ...... - 208 -
6.2. Sensor design and fabrication ...... - 212 -
6.3. Technical basis and procedure of scour monitoring using the innovative
TDR sensor ...... - 214 -
6.4. Field deployment of the TDR scour monitoring system ...... - 218 -
6.4.1. System Design ...... - 218 -
6.4.2. Field Deployment...... - 220 -
v
6.5. Long-term performance of the system ...... - 222 -
6.5.1. Preliminary Data Analysis ...... - 223 -
6.5.2. Challenges and Pitfalls ...... - 226 -
6.6. Summary and conclusions ...... - 227 -
Chapter 7 Summary, Conclusions and Future work ...... - 229 -
7.1. Summary and Conclusions ...... - 229 -
7.1.1. CFD modeling of the effect of pier configurations on flow and
scour pattern ...... - 229 -
7.1.2. Bio-inspired hair flow sensor ...... - 231 -
7.1.3. TDR field bridge scour monitoring system ...... - 232 -
7.2. Future work ...... - 233 -
7.2.1. On CFD modeling ...... - 233 -
7.2.2. On biomimetic flow sensor ...... - 234 -
7.2.3. On field bridge scour monitoring system...... - 235 -
Reference ...... - 236 -
vi
LIST OF TABLES
Table 3.1. Details for the Test Cases ………………………………………………...- 70 -
Table 4.1. Summary of Different Designs of Piezoresistance
Based MEMS BHFSa...... - 136 -
Table 4.2. Summary of Different Designs of Capacitance Based BHFS
developed by the group in Twente ...... - 142 -
Table 6.1. Example calculations using the algorithm elaborated in Figure 6.3...... - 223 -
vii
LIST OF FIGURES
Figure 1.1. Illustration of the contraction scour and local scour at a bridge ...... - 3 -
Figure 1.2. The primary turbulence structures around a circular cylinder ...... - 4 -
Figure 1.3. A schematic illustration of the forces exerted on a sediment
particle in flow...... - 7 -
Figure 1.4. Three types of sediment transported in the stream ...... - 11 -
Figure 1.5. Scour hole surrounding bridge piers ...... - 12 -
Figure 1.6. Illustration of the outline of the dissertation ...... - 16 -
Figure 2.1. The organization of this review on CFD models for
scour related problems...... - 20 -
Figure 3.1. The meshing elements of the computation domain ...... - 65 -
Figure 3.2. The streamlines and velocity vectors upstream of the cylinder...... - 66 -
Figure 3.3. Streamlines and velocity vectors on the horizontal planes at different
vertical locations...... - 67 -
Figure 3.4. Pressure distributions along (a) the upstream stagnation line and (b) the
symmetry line on the bed...... - 68 -
Figure 3.5. The mean bed shear stress along the symmetry line upstream
of the cylinder...... - 69 -
Figure 3.6. Limited streamlines around piers with cross-sectional shapes of
circular (a), square (b), diamond (c) and lenticular...... - 72 -
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Figure 3.7. Vertical velocity distributions along the symmetry line in front of
the pier (a) and along the transverse cut line near the bed in front
of the pier (b)...... - 73 -
Figure 3.8. Contour of the normalized bed shear stress near the piers with
different shapes...... - 75 -
Figure 3.9. Scour pattern obtained by numerical simulation (upper parts) and
corresponding experiments for piers with different cross-sectional
shapes. (Adapted from Khosronejad et al. (2012)) ...... - 76 -
Figure 3.10. Limited streamline on the plane H/20 over the bed for the oblong piers
with L/B=2(a) and L/B=7(b) ...... - 79 -
Figure 3.11. Vertical velocity distributions along the transverse cut line near the
bed in front of the pier...... - 79 -
Figure 3.12. Normalized τmax for piers with different aspect ratios ...... - 80 -
Figure 3.13. Normalized shear stress near the rectangular piers with different aspect ratios:...... - 81 -
(a): L/B=2 (b) L/B=5 and (c) L/B=7...... - 81 -
Figure 3.14. Sketch of the scour pattern around piers with different aspect ratios...... - 82 -
(Adapted from Briaud et al. (2004)) ...... - 82 -
Figure 3.15. Limited stream line around round-nosed oblong piers with different
attack angle (L/B=4): (a) α=30° (b) α=60° and (c) α=90° ...... - 84 -
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Figure 3.16. Normalized bed shear stress around round-nosed oblong piers with
different attack angle (L/B=4): (a) α=30° (b) α=60° and (c) α=90° ...... - 85 -
Figure 3.17. The maximum shear stress ratio, the scour critical zone area ratio
and the weighted scour critical zone area ratio at different attack angles
(round nose). (a) L/B=2 and (b) L/B=4...... - 86 -
Figure 3.18. The maximum shear stress ratio at different attack angles and
corresponding fitting curves...... - 87 -
Figure 3.19. Sketch of the scour pattern around piers with attack angle of 15°
(a) and 30° (b) (Adapted from Briaud et al. (2004)) ...... - 89 -
Figure 3.20. The flow chart for modeling of the scour process ...... - 93 -
Figure 4.1. The lateral line system of fishes...... - 112 -
Figure 4.2. Schematic illustrations of CNs and SNs and their responses to
hydrodynamic stimulus...... - 117 -
S Figure 4.3. Multiple-layer filtering of a CN to a vibrating sphere. and YUc ...... - 121 -
Figure 4.4. Multi-layer filtering of a SN to a pressure driven flow ...... - 125 -
Figure 4.5. Piezoresistance based MEMS hair sensors from the MedX Lab.
second design...... - 131 -
Figure 4.6. The schematic drawing of the capacitive hair sensors ...... - 139 -
Figure 4.7. Different designs of capacitive hair sensors ...... - 139 -
Figure 5.1. Schematic drawing of the proposed sensor. (The sensor consists of a
piezoelectric fiber coated with a pair of separated electrodes; the
x
deformation of the fiber generates charges, which can be collected
and recorded through the electrodes. The directions 1,2,3 are used
in the subsequent discussions in this paper.) ...... - 152 -
Figure 5.2. The cross section of the hair sensor...... - 154 -
Figure 5.3. FEM modeling of the proposed sensor design...... - 158 -
Figure 5.4. The predicted directional sensitivity of the proposed sensor design...... - 160 -
Figure 5.5. (a) schematic of sputtering Ag layer on the piezoelectric fiber; (b) the
piezoelectric fiber with electrodes connected to wire leads;
(c) the fabricated hair sensor was mounted on an in-house built
angle controller...... - 161 -
Figure 5.6. Laboratory evaluation of the directional responses of the hair sensor. ... - 162 -
Figure 5.7. Maximum amplitudes of sensor signals under different loading
conditions...... - 164 -
Figure 5.8. The schematic illustration of the proposed design of the bio-inspired
flow sensor and its principle...... - 166 -
Figure 5.9. Analytical model for the transduction mechanism of the proposed
hair sensor...... - 168 -
Figure 5.10. FEM model for the performance of the sensor element...... - 170 -
Figure 5.11. A fabricated biomimetic “hair” sensor in macro scale...... - 174 -
Figure 5.12. Laboratory setup for the characterization of the hair sensor...... - 176 -
Figure 5.13. Sampled signals of the sensor under different loading conditions...... - 176 -
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Figure 5.14. Results of measured sensor signals...... - 177 -
Figure 5.15. (a) the measured response signals from two hair sensors aligned with
different spacing subjected to burst-induced air flows (the hair
sensor in the upstream of the burst is noted as “US” and the one in
downstream as “DS”);
(b) the relationship between the spacing of the two hair sensors and
corresponding measured time delays...... - 178 -
Figure 5.16. The design of the hair sensor with artificial cupula...... - 182 -
Figure 5.17. Equivalent components of the composite sensor ...... - 184 -
Figure 5.18. Sensitivity of the sensor: a) with different n, η and μ;
b) with different η and μ, while n=4
c) with different n and μ, while η=60...... - 185 -
Figure 5.19. The meshed domains and the electrical boundary conditions ...... - 189 -
Figure 5.20. The linearity (a) and the directional sensitivity (b) of the sensor ...... - 189 -
Figure 5.21. (a) The calculated neutral axis locations (a) and average strain on the
centroid axis (b) for different host materials with different models ...... - 191 -
Figure 5.22. The hair sensor connected to a shunt circuit...... - 194 -
Figure 5.23. Four configurations of the shunt circuit is studied ...... - 196 -
Figure 5.24. Sensor with an R only circuit:
The spectrum response curve (a)
and the effect of the resistance on the peak value (b)...... - 198 -
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Figure 5.25. Sensor with an L only circuit: The spectrum response curve...... - 199 -
Figure 5.26. Sensor with a parallel RL circuit:
The spectrum response curve (a) and
the effect of the inductance on the peak value (b)...... - 201 -
Figure 5.27. Sensor with a RL circuit in series:
The spectrum response curve (a) and
the effect of the inductance on the peak value (b)...... - 203 -
Figure 5.28. Comparison of the spectrum response curves ...... - 204 -
Figure 6.1. The newly designed field TDR bridge scour sensor.
(a) The schematic drawing of the cross-section of the sensor;
(b) The longitudinal view of the sensor; and
(c) the photo of the fabricated bridge scour sensor (one portion of the
E-glass U-channel is cut to expose the TDR strip)...... - 213 -
Figure 6.2. The laboratory setup of the scour sensing (a)
and the sample TDR signals (b)...... - 215 -
Figure 6.3. The procedure to determine the scour depth through the TDR signals. . - 218 -
Figure 6.4. Schematic Diagram of the Real-time TDR Field Bridge Scour
Monitoring System...... - 218 -
Figure 6.5. The locations of the installed TDR sensors at the BUT-122-0606
Bridge on State Route 122 over the Great Miami River...... - 220 -
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Figure 6.6. (a) Installation of the field TDR sensor using traditional geotechnical
equipment and procedures; and
(b) The installed field control unit...... - 221 -
Figure 6.7. Sample signals of the field TDR sensor. The reflection points and
the change of the probe end reflection are clear...... - 222 -
Figure 6.8. Scour evolution at Location 1 during the first two months...... - 224 -
Table 6.2. The cumulative scour depths at the five locations
2 months after installation...... - 224 -
Figure 6.9. (a)The stream discharge record of the river at the bridge
(data from USGS website) between November 2010 to April 2012;
(b) Monitored scour/sedimentation process during the same time-span. - 225 -
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ACKNOWLEDGEMENT
When I was a kid, I read a lot of stories of great scientists. I found they had one thing in common: they all had an academic advisor who changed their lives. Even though I am not that successful yet, I am fortunate to have one such advisor in my life. I owe my sincerest gratitude to Prof. Bill Yu, a true mentor, a role model and a real friend of mine.
Bill guided me to the world of research and influenced my career path. He gave me the privilege to work on this interdisciplinary project and enlightened me on how to become a successful researcher. Without his support, encouragement, trust and guidance, I could not have become who I am today. Bill’s open mind, diligence and ever-positive attitude are always inspiring to me. He is also always ready to give a hand whenever I need it. I am blessed that our friendship has kept on growing and is worth cherishing for a life time.
This dissertation cannot have been completed without the support and help from my committee members. I cannot forget Dr. Adel Saada’s encouragement before and after my qualifying exam. Dr. Saada’s enthusiasm and passion in education also makes himself a role model. I am also impressed and inspired by Dr. David Zeng’s wealth of knowledge in geotechnical engineering. I would also like to thank Dr. Jaikrishnan Kadambi for sharing his knowledge in fluid dynamics. My gratitude also goes to Dr. Chung-Chiun Liu for his insightful advices and generous help during the development of the hair sensors.
I would also like to thank all the collaborators, engineers and colleagues, without whom my dissertation work could not have been done. My gratitude goes to Dr. Xinbao Yu for his selfless sharing of his research findings in the area of TDR scour sensor. I also would like to thank Jim Berilla from Civil Engineering department and Laurie Dudik from
xv
Electronic Design Center at Case for their help in the fabrication of the hair sensors. I am also grateful for having the opportunities to discuss with Dr. Liming Dai and his student
Mr. Feng Du in the Department of Macromolecular Science and Engineering. They expanded my perspective in interdisciplinary researches and introduced me to the world of nanotechnology. My appreciation also goes to Nancy Longo, who helped proof read every paper I published.
I would also like to take this opportunity to thank all my friends and colleagues at Case, especially Dr. Bin Zhang, Dr. Yan Liu, Dr. Chunmei He, Dr. Bo Li, Dr. Zhen Liu, Hao
Yu, Ye Sun, Yuru Li, Guangxi Wu, Jianying Hu and Quan Gao. They made my four years in Cleveland unforgettable. Their friendship makes me grateful for life.
I am always indebted to my dad, mom, brothers and sister in law. Their continuous love, caring, support and sacrifice drive me to keep moving forward. They always refuel me with the courage and wisdom to overcome any hardship encountered in life.
Finally, I would like to thank another person who changed my world. She is my girlfriend, my soul mate and my inspirational source, Liangliang Huang. Liangliang is the motivation why I strive and fight so hard; she is always the powerhouse when I feel lack of faith and energy. It is she who teaches me what love is and how magic it is. Thanks for tasting every bitter and sweet piece of life with me.
This dissertation work is supported by National Science Foundation (CMMI-0846475,
CMS 0900401) and Ohio Department of Transportation (No. 134374). The supports are acknowledged.
xvi
LIST OF ABBREVIATIONS
1-D: One Dimensional
1-DOF: One Degree of Freedom
2-D: Two Dimensional
2-DOF: Two Degree of Freedom
3-D: Three Dimensional
AC: Alternating Current
ADV: Acoustic Doppler Velocimetry
ALE: Arbitrary Lagrangian-Eulerian
BHFS: Biomimetic Hair Flow Sensors
CFD: Computational Fluid Dynamics
CN: Canal Neuromast
CNT: Carbon Nanotubes
DC: Direct Current
DDES: Delayed Detached Eddy Simulations
DEM: Discrete Element Method
DES: Detached Eddy Simulation
DES-LR: Detached Eddy Simulation-Low Reynolds
DOT: Department of Transportation
EFA: Erosion Function apparatus
FEM: Finite Element Method
FOM: Figure of Merit
FSI-CURVIB: Flow-Structure Interaction Curvilinear Immersed Boundary
FVM: Finite Volume Method
FVPM: Finite Volume Particle Methods
FHWA: Federal Highway Administration
HEC: Hydraulic Engineering Circular
xvii
HV: Horseshoe Vortex
HWA: Hot Wire Anemometer
IDE: Interdigitated Electrodes
IMPC: Ionic Polymer-Metal Composites
LED: Light Emitting Diode
LES: Large Eddy Simulations
MEMS: Microelectromechanical systems
MLP: Multilayer Perceptron
MPS: Moving Particle Semi-implicit
NBIS: National Bridge Inspection Standards
NCHRP: National Cooperative Highway Research Program
NEMS: Nano Electro-Mechanical Systems
NV: Necklace Vortex
ODE: Ordinary Differential Equation
OSC: Oscilloscope
PC: Personal Computer
PDE: Partial Differential Equation
PDMA: Plastic Deformation Magnetic Assembly
PEG: Polyethylene Glycol
PEG-TA: Poly(ethylene glycol) tetraacrylate
PFEM: Particle Finite Element Method
PIV: Particle Image Velocimetry
PTFE: Polytetrafluoroethylene
PVDF: Polyvinylidene fluoride
PZT: Lead zirconium titanate
RANS: Reynolds-Averaged-Navier-Stokes
Re: Reynolds
RL: Resistor-inductor
xviii
RNG: Renormalization Group
RSM: Reynolds Stress Model
S-A: Spalart-Allmaras
SDW: Spiral Double Wire
SGS: Sub-Grid Scale
SN: Superficial Neuromast
SPH: Smoothed Particle Hydrodynamics
SPICE: Simulation Program with Integrated Circuit Emphasis
SRICOS: Scour Rate In Cohesive Soils
SSIIM: Sediment Simulation In Intakes with Multiblock
SST: Shear-Stress Transport
TDR: Time Domain Reflectometry
URANS: Unsteady Reynolds Averaged Navier Stokes
USGS: United States Geological Survey
UV: Ultraviolet
VOF: Volume of Fluid
WALE: Wall-adapting local eddy-viscosity
ZNO: Zinc Oxide
xix
Fusion of Numerical Modeling and Innovative Sensing to Advance Bridge Scour Research and Practice
by
JUNLIANG TAO
ABSTRACT
Bridge scour is the erosion of sediments around bridge piers or abutments due to flowing water. It is the number one cause of bridge failures in the United States. However, the mechanism of bridge scour remains a mystery due to the complex interaction between structures, flow, and sediments; there is also an urgent demand to develop countermeasures reducing the risk caused by bridge scour. This dissertation work aims to provide innovative solutions to address such challenges through highly interdisciplinary efforts. A tremendous effort has also been placed to review and synthesize the existing literature.
Computational Fluid Dynamics (CFD) technique is employed to simulate the flow and scour patterns around bridge piers with different geometries. The effects of pier shape, aspect ratio and attack angle on the flow and scour patterns are evaluated. The findings of this work not only further advance the understanding of scour, but also provide insightful practical implications. A numerical simulation framework integrating advanced CFD techniques and a novel sediment transport model is also developed, aiming to model the scour process. The uniqueness of this advanced model is that it incorporates the influence of turbulence, which plays a crucial role in the process of scouring but has been overlooked for decades.
xx
To facilitate the characterization of the turbulence at the interface of sediment and river flow, bio-inspired flow sensors are developed. The innovative sensors mimic the function and structure of the hair cells in fish, which is sensitive to turbulence in flow. Smart material (piezoelectric microfiber) is employed to construct the artificial hair cell and the unique patterning of electrodes enables the linear sensitivity as well as the directional sensitivity of the sensor. Three designs are proposed, modeled and optimized. The performance of the prototype sensors is evaluated through laboratory experiments.
A field monitoring system is designed and deployed in the field to remotely monitor the evolution of the scour depth around real bridge piers. This system includes an innovative sensor based on Time Domain Reflectometry (TDR) technique and the sensor is proved to be sensitive, durable and cost effective. It also includes a field data acquisition system, which automatically collects the TDR data and transmits the data wirelessly. The scour depth data can be utilized to calibrate the various scour depth prediction equations. It can also be integrated into the bridge risk management system to assist in decision making.
xxi
CHAPTER 1
INTRODUCTION
1.1. BACKGROUND
Bridge scour has been identified as the major cause for bridge failures in the United
States for a long time and it remains a stubborn adversary to engineers. The erosion of
soil around the bridge foundations may leave the superstructures without enough support
and could eventually lead to complete collapse of the bridge. A recent National
Cooperative Highway Research Program (NCHRP) report revealed that during the time
span of 1966-2005, 58% of the reported bridge failures (1,502 in total) were ascribed to
scour (Hunt 2009).
The consequences of bridge scour are self-evident: disruption of the transportation network, direct costs for replacing and restoring of the structure, indirect costs suffered by the general public, and the worst situation, loss of lives. Prominent examples of catastrophic collapse of bridges due to scour include the Schoharie Creek Bridge in the state of New York (1987, 10 fatalities), the Walker Bridge over Hatchie River near
Memphis, Tennessee (1989, 8 fatalities) and the I-5 over Los Gatos Creek in California
(1995, 7 fatalities) (more information in Arneson et al. 2012). Twenty three bridges failed due to the 1993 flood in the upper Mississippi basin, resulting an estimated damage of $15 million; Over five hundred bridges were damaged during the 1994 flooding from the Alborto storm in Georgia, causing a total damage to the Georgia Department of
Transportation highway system of approximately $130 million.
- 1 -
Clearly, bridge scour is a crucial problem for bridge safety and has received national
attention. During the past several decades, research has been conducted to advance the
design, countermeasures, evaluation and inspection of bridge scour. The Federal
Highway Administration (FHWA) issued a set of Hydraulic Engineering Circulars (HECs)
guiding the design and analysis of bridge scour and stream stability. These HECs include
HEC-18 (Evaluating Scour at Bridges), HEC-20 (Stream Stability at Highway Structures)
and HEC-23 (Bridge Scour and Stream Instability Countermeasures). Through the past
several decades, HEC-18, HEC-20 and HEC-23 has been revised, updated and advanced
to the fifth edition (Arneson et al. 2012), the fourth edition (Lagasse et al. 2012) and third
edition (Lagasse et al. 2009), respectively. As a Federal regulation, the National Bridge
Inspection Standards (NBIS) require bridge owners to maintain a bridge inspection
program for bridges which are identified as scour critical bridges (NBIS 23 CFR
650.313.e.3). The importance and complexity of this problem is the motivation of this
dissertation.
1.2. BRIDGE SCOUR BASICS
1.2.1. Definition and Components
Scour is an engineering term describing the erosion of sediments caused by flowing water
(Arneson et al. 2012). At a bridge crossing in the riverine environments, the total scour
primarily includes three components: long-term degradation; contraction scour and local scour at bridge piers or abutments (Figure 1.1). In some specific situations, there may be other types of scour as well as lateral migration of the stream.
- 2 -
Long-term degradation is the lowering of the riverbed over relatively long reaches when
the sediments supply from the upstream is less than the eroded sediments.
Figure 1.1. Illustration of the contraction scour and local scour at a bridge (Wang, 2004)
Contraction scour is caused by the reduction of the flow area of a stream. The
acceleration of the flow due to the flow area reduction results in the increase of the bed
shear stress on the riverbed, enhancing erosion of sediments. There are various factors which are responsible for contraction scour, such as natural stream constrictions, bridge piers and abutments, long highway approaches to the bridge over the floodplain, debris and ice jams and etc. (Arneson et al. 2012).
Local scour is the erosion in the vicinity of the bridge piers or abutments due to the formation of turbulence structures in various scales in that region. The turbulence structures amplify the bed shear stress exerting on the riverbed; the interactions among turbulence structures will further make the condition more complex (Arneson et al. 2012).
- 3 -
Contraction and local scour are traditionally classified as clear-water scour and live-bed
scour. Clear-water scour condition is characterized as scour when the approaching flow
doesn’t convey sediments to the scouring area; while live-bed scour occurs when the
upstream flow transports bed material to the scouring area. During a flood event, bridge
piers or abutments seated in coarse bed materials are usually subjected to different scour
conditions depending on the flow discharge: clear-water scour at low discharges, live-bed
scour at high discharge and clear-water scour again in the recession stage. Live-bed scour is cyclic in that the scour hole deepens during the rising stage of a flood and refills during the recession stage (Arneson et al. 2012).
1.2.2 Typical turbulence structures around a circular cylinder
Figure 1.2. The primary turbulence structures around a circular cylinder (Ettema et al. 2011)
1.2.2.1. Coherent turbulence structures
- 4 -
In the real riverine environment, the flow discharging (approaching velocity and flow depth) varies from time to time and therefore the turbulence structures is also unsteady and changes from time to time. Although unsteady, a few features of the turbulence structures are kept organized. The organized turbulence structures are traditionally termed as coherent structures.
Experimental researches (Dargahi, 1989, Graf and Istiarto, 2002, Chrisohoides and
Sortiropoulos, 2003, Chrisohoides et al., 2003, Barbhuiya and Dey, 2004, Dey and
Barbhuiya, 2006, Unger et al., 2007, Dey and Raikar 2007) have unveiled the typical coherent turbulence structures developed in the immediate neighborhood of obstacles in flow. Figure 1.2. shows a schematic drawing of the flow field around a circular cylinder sitting in the sediments. The main flow structures include: 1) the downward flow and upward flow in front of the cylinder; 2) the horseshoe vortex around the cylinder near the riverbed; 3) the separated shear layers along each flank of the cylinder; and 4) the wake vortices convected through the cylinder’s wake.
1.2.2.2. The development of the turbulence structures
The approaching flow is assumed as fully developed turbulent shear flow. Therefore, the velocity follows an exponential distribution in the direction perpendicular to the riverbed, as the velocity at the free surface is the mean velocity and the velocity at the riverbed is zero. When the flow approaches the cylinder, it decelerates in front of the cylinder and due to the vertical velocity gradient, a downward flow forms toward the riverbed; at the same time, an upward flow is formed toward the free surface. The upward flow interacts with the free surface flow, forming the surface roller. The downward flow impacts the
- 5 -
riverbed and interacts with the incoming flow, forming the macro-scale necklace vortices
or the horseshoe vortex system at the base of the conjunction. The horseshoe vortex system wraps around the base of the bridge foundation with its legs orienting approximately parallel to the approaching flow. The flow converges, contracts and then diverges, producing the detaching shear layer and wake vortices. The detaching shear layer consists of small but energetic elongated eddies, whose axis is approximately
perpendicular to the riverbed (vertical). The wake vortices are convected downstream,
dissipating and breaking up with expanding diameters.
In recent years, the state-of-art Computational Fluid Dynamic (CFD) techniques have
been adopted to study the dynamics of the three dimensional coherent vortex structures
around obstacles in an open channel. These models can be used to capture the bimodal
dynamics of the vortex structures, which have significant implications to scour
mechanism around bridge piers. It was found that, the bimodal, low frequency
oscillations of the horseshoe vortex system produces much higher turbulent energy and
stresses near the bed than those produced by the conventional shear mechanism in the
approaching turbulent boundary layer (Paik et al. 2007); also found was the fact that the
instantaneous shear/friction velocity (equivalent to bed shear stress) on the bed had
significant temporal variations (Escauriaza and Sotiropoulos 2011a, b, c, Kirkil et al.
2009, Koken and Constantinescu 2009, Kirkil and Constantinescu 2009, 2010).
Sometimes the instantaneous velocity would be as much as 6 times that of the time averaged velocity (Escauriaza and Sotiropoulos, 2011a, b, c) and the standard deviation of the instantaneous friction velocity is comparable to the mean velocity (Koken and
- 6 -
Constantinescu 2009). A state of art review on the CFD modeling of flow and scour around bridge foundation structures is presented in Chapter 2.
Despite the velocity and depth of the approaching flow, the flow structures are also dependent on other factors such as the geometry of the obstruction and debris or ice jams.
The author classifies such problems as the flow-structure interaction. It is clear that the flow field around obstructions in streams is truly three dimensional; there exist turbulent vortex structures with different patterns and scales, which also interact with each other.
Exposed to such a complex flow condition, the sediment particles are dislodged from the river bed and transported in a combination of motions such as rolling, sliding and plucking (Briaud et al., 1999).
1.2.3. Erosion and Sediment transport
1.2.3.1. Forces exerted on a sediment particle
Figure 1.3. A schematic illustration of the forces exerted on a sediment particle in flow: C.G. denotes the center of gravity; W denotes the weight of the soil particle. uw is the fluctuating water pressure around the
soil particle; τ is the flow induced drag force or shear stress; Flift is the flow induced lift force; fci is the
contact forces between particles and fei is the electrical forces between particles.
- 7 -
Erosion initiates when the sediment particles are dislodged by the flow. To unveil the mechanism of the scour process, the prerequisite is to identify the forces imparted on the sediments. Figure 1.3 provides a schematic illustration of the forces.
The sediment particles are subjected to drag and lift forces by the flow. Precise description of such forces is a non-trivial problem since the forces are significantly influenced by turbulence structures with various scales. Despite the macroscopic coherent vortex structures, the microscopic flow structures and hydrodynamic forces has also been identified through advanced experiments (Diplas et al. 2010; Dwivedi et al. 2010, 2011).
Through measuring the instantaneous pressures around single particles (12.7mm), the drag and lift forces imparted on the particle are found to be correlated to each other and are both correlated to the near bed streamwise velocity (Diplas et al. 2010). Coherent turbulent events (i.e. outward interactions, ejections, inward interactions and weeps) are also identified through direct measurement of hydrodynamics forces and velocity on a particle (Dwivedi et al. 2010, 2011); quadrant analysis and probability distribution functions of the turbulent forces indicate that the sweep events are mainly responsible to the entrainment of the particle. The experiments are typically conducted in flumes without obstructions in them. For bridge scour, it is expected that the statistical characteristics of the microscopic flow events are different from that in unobstructed flows.
The resistance forces are different for different sediments. For cohesionless sediments, researchers treate the friction force between particles and the gravitational force as the scour resistance forces. For cohesive sediments, scientific explanations of its erosion are lacking. This is probably due to the complex nature of the inter-particle forces, or
- 8 -
cohesion, in cohesive sediments. The resistive forces in cohesive sediments arise from
molecular-scale physicochemical attractive forces including hydrodynamic viscous drag
force, van der Waals attraction, electrical double-layer repulsion and Born’s repulsion
(Anderson and Lu, 2001).
1.2.3.2. Initiation of erosion
Widely used “excess shear stress” concept
Based on data from flume test with flat bed and undisturbed channel flow, Shields (1936)
* found that the non-dimensional critical shear stress τcrit can be related to the Reynolds
number (Red*) of the particles through a curve which is refereed as Shields curve
thereafter. The non-dimensional shear stress is defined as the ratio of the shear force Fμ to
the effective weight G’ of the sediment subjected to this shear force Eq. 1.1 (Zanke,
2003).
τ F A τ* = b = const μ (1.1) ρ (s−1) gd G' A
The Shields parameter is widely adopted for erosion and scour problems for decades,
despite there are numerous variation of the original Shields curve (e.g., Yalin 1972,
Zanke 1996 and Soulsby 1997). The premise of the excess shear stress concept is that, at least in non-turbulence flows, the sole driving force for the initiation and transport of sediments is the shear stress; the only resistance of the sediments is provided by the gravity.
Recent progresses
- 9 -
For a long time, researchers have realized the limitations of the excess shear stress criteria for erosion. But only until recently has researchers begun to explore more details about the fundamental mechanism of soil erosion. Experiments on the initiation of 12.7- mm Teflon spheres in turbulent flow indicated that peak value of the fluctuating velocity is necessary but not sufficient to cause a sphere to dislodge (Diplas et al. 2008). This leads to the development of a theory in which the product of force magnitude and its duration, or the impulse, governed the dislodgement of a particle in the turbulence flow
(Diplas et al. 2008, Celik et al. 2010, Vlyrakis et al. 2011a,b). This impulse criterion was extended to characterize different incipient motions of particles, such as salating and rolling of an individual particle (Vlyrakis et al. 2010).
Work/energy based criteria for grain dislodgement in turbulent flow are also explored for individual particle dislodgement. Viewing the geometric pocket formed by the surrounding particles as a potential well where the energy barrier is imposed by the gravitational and frictional mechanism of the target particle, the dislodgement and migration of the particle can be evaluated using a work-based criterion (Lee et al. 2012).
When the work done by the hydrodynamic forces surpasses this energy barrier, the particle will dislodge from the pocket (potential well) and be mitigated downstream.
Another energy based criteria is evolved from the impulse criterion. In this criterion, sufficient power provided by the hydrodynamic forces and its duration will accomplish the particle entrainment (Valyrakis et al. 2013).
These newly developed criteria significantly advanced our understanding on the initiation of single particles in turbulent flow.
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1.2.3.3. Sediment transport modes
The sediments transported in the stream are traditionally categorized into three different types: bed load, suspend load and dissolved load (Figure 1.4).
Dissolved Load
Suspended Load
Bed Load
Figure 1.4. Three types of sediment transported in the stream1
Bed load is the sediments transported near the river bed and the movement of such sediments is usually rolling, sliding and saltating. Bed load moves with a small fraction of the mean flow velocity. The bed load rate is traditionally descripted using the excess shear stress concept. It is widely accepted that when the excess shear stress is small, bed load is the only bed material load.
Suspended loads are the sediments transported in the lower to middle part of the flow, and it moves at a large portion of the mean flow velocity. When the excess shear stress is large enough, sediment particles may be suspended by the turbulence flow. The suspended load rate is dependent on the settle velocity or fall velocity of the particle.
1 http://en.wikipedia.org/wiki/File:Stream_Load.gif
- 11 -
Dissolve load is the disassociated ions moving with the flow. Strictly speaking, it is not sediment, but it may constitute a significant portion of materials transported with flow2.
To determine the elevation change of the riverbed, the bed load and suspended load is needed to be calculated. In the vicinity of a bridge pier, rich turbulent structures develop and will interact with the sediment particles. This makes the prediction of bed elevation change very challenging. The author categorizes the sediment transport problem as the flow-sediment interaction problem.
1.2.4. Scour hole development
(a) (b)
Figure 1.5. Scour hole surrounding bridge piers: (a) at the Schoharie Creek Bridge, 1987 (Lagasse, 2009);
(b) at the Platte River Bridge, 20103.
The development of a scour hole is the result of the elevation change of the riverbed surrounding the bridge foundation structures. In practice, the scour hole depth is an important indicator to evaluate the severity of the scour. Schoharie Creek bridge
2 http://en.wikipedia.org/wiki/Sediment_transport
3 http://thestagnationpoint.blogspot.com/2010/09/scour-hole-platte-river-maxwell.html
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collapsed in 1987 due to severe scour in the flood. The scour depth around one of the piers at failure was 14 ft (4.3 m) (Lagasse 2009, Figure 1.5).
Scour hole may have different geometries (e.g., in Figure 1.5a,b). There are a variety of factors affecting the scour depth around bridge piers and abutments: 1) velocity and depth of the approaching flow; 2) geometry of the pier; 3) angle of the attack of the approaching flow to a pier or abutment; 4) bed material properties; 5) bedform configuration as well as 6) ice formation or accumulation of debris.
For different bed materials, the scouring rate might be different. For example, coarse sand can be eroded much more rapidly than cohesive or cemented soils, with all the other conditions the same. However, the maximum scour depth in cohesive soils can be similar in sand-bed streams (Arneson et al., 2012). With the development of the scour hole, the flow field also alters and this results in the reduction of the shear stresses on the sediments. There is an equilibrium condition when the shear stress is lower than the critical shear stress and scour ceases.
Based on laboratory experiments, various scour prediction equations have been proposed
(Breusers et al. 1977; Briaud et al. 1999; Laursen and Toch 1956; Melville and Chiew
1999; Richardson and Davis 2001; Shen et al. 1969; Sheppard et al. 2004; Debnath and
Chaudhuri, 2012). These equations predict the maximum scour depth considering the structure, sediment and flow conditions and can be written in a uniform equation in the dimensionless form as shown in Eq. 1.2 (Sturm 2001).
d y Vρ Vb V b s = fKK,,,1 1 , 11 ,, ,σ (1.2) sgθ µ b b gy1 Vdc 50
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Where ds is the equilibrium scour depth; b is the width of the bridge pier; Ks, Kθ is the
shape facto and alignment factor, respectively; y1 and V1 are approach depth and velocity,
respectively; Vc is the critical velocity for initiation of sediment motion in the approach
flow; g is the acceleration due to gravity; d50 is the median sediment size; σg is the geometric standard deviation of sediment size distribution; µ and ρ is the dynamic viscosity and density of the fluid.
The whole scour process is a dynamically interacting process: the changing of the scour hole is caused by the flow field, which will also be altered in turn. The author classifies this process as the flow-bedform interaction.
1.3. RESEARCH OBJECTIVES
The previous context illustrated the importance of bridge scour problem (Section 1.1),
presented the basics of bridge scour, including the flow-structure interaction, flow-
sediment interaction and flow-bedform interaction. To fully unveil the mechanism of bridge scour, there remain research efforts to investigate each of these three thrusts. This
dissertation is an effort integrating numerical simulation and innovative sensing
techniques to address the following objectives:
(1) To investigate the effect of bridge pier configurations on the flow field and
scour pattern; (Flow-structure interaction)
(2) To develop sensing technology for measuring and characterizing the turbulent
flow in different scales; (Flow-structure interaction; flow-sediment interaction)
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(3) To develop a sensor for field monitoring of bridge scour. (Flow-bedform
interaction)
Objective (1) is addressed by numerical modeling utilizing three dimensional
Computational Fluid Dynamics (CFD) techniques; objective (2) is addressed by
designing a biomimetic sensor inspired by the hair sensors in fish lateral line system;
objective (3) is addressed by deploying and evaluating a field bridge scour probe based
on Time Domain Reflectometry (TDR) technology.
The dissertation work contains both research and practical significance. The modeling of
flow field around bridge piers with different configurations helps to reveal the complex turbulence structures; through the comparison between the flow patterns and scour patterns, it is expected to advance the mechanism of bridge scour. The evaluation of the effects of bridge pier shapes and alignment would provide insights on the design and countermeasure of bridge scour. The introduction of an innovative bio-inspired flow sensor will facilitate the characterization of the turbulence flow, especially the turbulence at the flow-sediment interface. The scour monitoring system can provide field scour depth information for bridge risk management authorities; the field data can also be used to calibrate the various scour depth prediction equations which are mostly developed with laboratory test (small scale) data.
1.4. ORGANIZATION OF THE DISSERTATION
This dissertation is organized into five parts and seven chapters (Figure 1.6).
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Figure 1.6. Illustration of the outline of the dissertation
The first part is Chapter 1. This chapter introduces the fundamentals of bridge scour. The flow field around bridge piers, the sediment transport and scour hole development is briefly reviewed, respectively. Also presented are the three objectives of this dissertation study. Each objective is addressed with a relatively independent part in the main context of the dissertation.
The second part consists of Chapter 2 and Chapter 3. This part intends to address the first objective: CFD modeling of bridge scour.
• Chapter 2 provides a synthetic review on the advances in the modeling of flow
and scour around hydraulic structures using CFD technique. Different modeling
strategies are characterized, reviewed, and compared. This chapter can serve as a
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comprehensive reference for both beginners and experts on the topic of CFD
modeling of bridge scour. It also serves as a guide to select proper modeling
strategies for different purposes.
• Chapter 3 is the application of the CFD technique to simulating the flow pattern
and scour around bridge piers. It includes a holistic assessment of the effect of
pier configurations on the flow patterns. Investigated are the factors such as pier
shape, pier length, pier width, pier aspect ratio and the attack angle of the
approach flow to the pier. The flow patterns are compared to the scour patterns,
shedding light on the mechanism of bridge scour. The practical implications are
also discussed. Despite the modeling of the flow field, a framework for the
simulation of the complete scour process is also developed. In this framework, the
influence of turbulence is incorporated in the sediment transport model.
The third part includes Chapter 4 and Chapter 5. This part is to address the second objective: design of a bio-inspired turbulence sensor.
• Chapter 4 provides a multi-disciplinary review on the hair flow sensors. It
includes an in-depth review on the biological hair flow sensors in the lateral line
system of fish. The morphology and sensing mechanism of the hair cells (canal
and superficial neuromasts) is elaborated. It also includes a comprehensive review
on the state-of-art artificial hair sensors.
• Chapter 5 is on the innovative hair sensor based on piezoelectric microfiber.
Three designs are proposed, including one with a pair of surface electrodes, one
with spiral-double-wire (SDW) electrodes and one with artificial cupula. The
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sensors all possess directional sensitivity as well as linearity in one direction.
These features are modeled using simplified analytical methods as well as more
sophisticate numerical models, which can take the fully-coupled piezoelectric
effect into account. The sensors are fabricated in macro size first and the
performance of the sensors is evaluated in the laboratory. In addition, the
optimization of the sensitivity and bandwidth of the third design is discussed in
details. An innovative approach (shunt circuit) to adapt the dynamic response of
the sensor is proposed and evaluated.
The fourth part includes Chapter 6. This part addresses the third objective: deployment and evaluation of a field bridge scour sensor. Chapter 6 presents a TDR field bridge scour sensor for long-term monitoring purpose. The design, fabrication, and the sensing algorithm are briefly introduced. The field monitoring system is deployed and the long- term performance of the system is evaluated.
The last part of the dissertation is Chapter 7. This chapter summarizes the main conclusions of this dissertation study and provides recommendations for the future work.
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CHAPTER 2
A SYNTHETIC REVIEW ON CFD MODELING OF BRIDGE SCOUR
Advancements in Computational Fluid Dynamics (CFD), including the improvements in
high efficiency algorithms and the fast growth of computing power, have empowered
new tools to study bridge scour phenomena.
Several reviews about scour are available in the literature (Breusers et al., 1977; Dey,
1997; Sumer et al., 2001; Sumer and Fredsøe, 2002; Sumer, 2007; Deng and Cai, 2010;
Briaud and Oh, 2010). Among these reviews, only Sumer (2007) focused on the
numerical simulation approach. Besides, it mainly focused on the basic ideas, general features and procedures for implementing the simulations. This Chapter is to review the progresses in the numerical simulations, to categorize common numerical approaches, and to compare the relative merits of different methods.
In Figure 2.1, the common types of CFD schema for bridge scour simulations are categorized into two branches. In the branch of single-phase models, the scour process, or the evolution of the scour hole morphology, is treated as a one-way coupling phenomenon with the change of the flow field. In such models, the flow field is firstly simulated with the initial river bed morphology using a hydrodynamic model, which is usually based on the Navier-Stokes equations (refer to Section 2.1 for details). The interface stress at the river bed is calculated from the simulated flow field. The rate of
- 19 -
river bed erosion is then estimated by use of a sediment transportation model. The bed
morphology is then updated based on the rate of erosion. Single-phase models are the
current prevailing methodology for scour simulations. Two-phase flow models treat the
sediment as a separate phase. Such models simultaneously couple the fluid and particle
phases, considering the interphasial interactions.
Figure 2.1. The organization of this review on CFD models for scour related problems.
This Chapter first reviews the computational basis of single-phase models for bridge
scour simulation. These single-phase models are reviewed based on the methods for
closure of the equation system for the CFD models, i.e., Reynolds-Averaged-Navier-
Stokes (RANS), unsteady Reynolds-Averaged-Navier-Stokes (URANS), Large Eddy
Simulation (LES) and Detached Eddy Simulation (DES). Selected examples of implementing these models for bridge scour simulations are described.
This Chapter then discusses the emerging two-phase flow models. The fluid flow (liquid phase) and sediment particles (solid phase) can be modeled either in an Eulerian formulation, a Lagrangian formulation or mix of Eulerian-Lagrangian formulation. This sets the basis for Eulerian-Eulerian models, Eulerian-Lagrangian models, and
- 20 -
Lagrangian-Lagrangian models in bridge scour simulations, respectively. There are
increasing interests in two-phase flow models for scour simulations in recent years.
Such categorizations are adopted only to make this Chapter more organized. The sub-
categorization for the single-phase models emphasizes on the different strategies for
turbulent flow modeling (Figure 2.1), which is a major challenge for scour modeling.
However, one should note that turbulence modeling plays an equal role in the two-phase
models and such turbulent strategies can also be applied.
To synthesize the past work, thorough discussions on the merits and limitations of the
common types of CFD models for bridge scour simulations are also provided.
2.1 SINGLE-PHASE MODELS FOR BRIDGE SCOUR MODELING
Single-phase models simulate the scour process as a one-way coupling between
hydraulic field and sediment transport. A typical single-phase model usually includes a
flow model and a bed morphological model. For a classic example of the procedure of
simulating bridge scour with a single-phase model, the readers are referred to Roulund et al. (2005). The key issue for single phase model is to model the hydraulic flow field, which typically involves solving the Navier-Stokes (NS) equations. This section reviews the CFD methods used in single-phase models, following the categorization by Spalart
(2000).
In general, the motion of fluid can be described by the classic Navier-Stokes equations
(Eq. 2.1), which include the continuity equation and the momentum equations.
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∂u i = 0 ∂ xi (2.1) ∂ ∂∂uu(uuij) 1 ∂∂p ∂u j ii+ =−+ν + +f ∂t ∂ xρ ∂∂ xx ∂ x ∂ x i j ij ji
In Eq. 2.1, ui is the flow velocity component in the xi (i=1, 2 or 3) direction, xj is the
coordinate (j=1, 2 or 3), p is the fluid pressure, fi is the volume force, and v is the fluid
viscosity.
Based on the advancements in CFD algorithms, the Navier-Stokes equations (Eq. 2.1) can be solved with different approaches; besides, the flow field around an obstacle can be simulated with adequate accuracy. Since the turbulence plays a crucial role on the entrainment and transport of the sediments near hydraulic structures, the accuracy in
simulating the scouring process is directly dependent upon the modeling of turbulence.
Spalart (2000) classified the methods and levels for the numerical prediction of a
turbulent flow. Such levels include Reynolds-Averaged-Navier-Stokes (RANS), unsteady
Reynolds-Averaged-Navier-Stokes (URANS), Detached Eddy Simulation (DES), Large
Eddy Simulation (LES) and Direct Numerical Simulation ( DNS). Definitions and
illustrations of these methods can be found in a variety of literatures about the
fundamentals of CFD (Wesseling, 2001; Launder and Sandham, 2002; Versteeg and
Malalasekera, 2007; Chung, 2010; Magoulès, 2011; Amano and Sundén, 2011).
Therefore they are only briefly introduced in the context of this Chapter.
Among these methods, DNS solves the Navier-Stokes functions directly with sufficiently fine meshes and sufficiently small time steps to resolve the smallest eddies and the fastest fluctuations (Versteeg and Malalasekera, 2007). However, DNS is extremely difficult to
- 22 -
perform due to the wide range of length and time scales in turbulent flow and the
computational cost it requires, which is typically far beyond the computational resources
available to most researchers. DNS is rarely applied to simulate the bridge scour
problems and therefore is not discussed in this Chapter.
2.1.1. Reynolds Averaged Navier-Stokes (RANS) models
RANS is an equation system representing the time-averaged motion of flow. It is derived from the Navier-Stokes equations (Eq. 2.1) by means of Reynolds decomposition (Eq.
2.2), in which the flow (ui) is decomposed into a time-averaged part ui (Eq. 2.3) and the
turbulence part u'i.
ui= uu ii + ′ (2.2)
+ 1 t0 T = uiilim ∫ utd (2.3) T→∞ T t0
The steady RANS equations can be expressed as Eq. 2.4, where the flow characteristics
are functions of the coordinates (for example, u= ux(,123 x , x )) and independent of time.
∂u i = 0 ∂ xi 2 (2.4) ∂∂uu1 ∂p ∂uuij′′ ufii=− +ν +− ji∂ρ ∂∂ ∂ xj xi xx jj xj
In Eq. 2.4, p and fi is the time averaged fluid pressure and the time averaged volume force, respectively.
Comparing Eq. 2.4 to Eq. 2.1, it was found that the decomposition introduces new terms
i.e., the Reynolds stresses (τρij≡ uu i′′ j ) to the equation system. The unknowns are now not
only the mean pressure term ( p ) and mean velocity components ( uvw, , ), but also the
- 23 -
turbulence stress terms ( u′22, v ′, w ′ 2 , uv ′′ , uw ′ ′ , vw ′ ′ ), which represents the interaction
between different turbulent fluctuations. The number of unknowns is 10, which is greater
than the number of equations, which is 4. Therefore, additional equations describing the
Reynolds stress are required to close the RANS.
The unsteady RANS (URANS) equations are similar to the steady RANS equations, but with the transient (time dependent) term retained (Eq. 2.5).
∂u i = 0 ∂ xi 2 (2.5) ∂∂uu1 ∂p ∂ u ∂uuij′′ ii+uf =− +ν i +− ∂ji ∂ρ ∂ ∂∂ ∂ t xj x i xx jj xj
The dependent variables are now not only a function of space coordinates, but also a
function of time (for example, u= ux(123 , x , x ,) t ). Similar to Eq. 2.2, Eq. 2.5 is also unclosed due to the Reynolds stresses term. And this is the well-known turbulence modeling or closure problem.
Most of the turbulence models are based on the concept of eddy viscosity and the presumption of an analogy between the action of viscous stresses and Reynolds stresses on mean flow (Versteeg and Malalasekera, 2007). The Boussinesq-type approximation between Reynolds stresses and the mean strain rate is presented in Eq. 2.6.
∂u ∂u j 2 τ=−++ ρν i ρk δ (2.6) ij t ∂∂ ij xxji 3
- 24 -
In Eq. 2.6, the first term on the right hand represents the effect of the eddy viscosity (νt)
∂ ∂ui u j and the mean strain rate ( + ); the second term involving the Kronecker delta (δij=1 ∂∂xxji
if i=j, otherwise δij=0) is the contribution of the turbulent kinetic energy per unit mass k
1 ( k= uvw′′22 ++ ′ 2) and this term ensures correct result for the normal Reynolds stresses. 2 ( )
Eq. 2.6 includes 6 equations. This together with Eq. 2.4 or Eq. 2.5 (4 equations each)
provides 10 equations, which is needed for the closure of the equation system to solve for
the 10 unknowns described in the previous context.
The core for the closure of the problem evolves to the modeling of the kinematic eddy
viscosity (νt) or the dynamic eddy viscosity ( µtt= ρν ). Based on the assumption that a
velocity scale (ϑ ) and a length scale (ℓ) is sufficient to describe the effects of turbulence,
dimensional analysis yields,
νϑt = C (2.7)
Eq. 2.7 has different forms for different modeling strategies for the eddy viscosity term.
There is a hierarchy of closure schemes, ranging from the zero-equation models to the two-equation models and the most complex Reynolds Stress Model (RSM).
Comparing the RANS models and the URANS models, the instantaneous flow is
decomposed into a stationary mean flow and a fluctuating turbulent component in RANS;
while in URANS, the instantaneous flow quantities such as velocity components and
pressure are decomposed in terms of a slowly varying unsteady mean and a high-
frequency turbulent component. Therefore, different from steady RANS, which can only
- 25 -
resolve the steady state flow characters with acceptable accuracy, URANS is capable of modeling the three-dimensional coherent vortices in turbulent flow, which plays a major role in scour phenomena.
The use of steady and unsteady RANS models to calculate the flow field around hydraulic structures has received significant attention due to its high computational efficiency.
Olsen and Melaaen (1993) and Olsen and Kjellesvig (1998) was among the first to simulate scour around a circular pile in three dimensions using CFD techniques. They used the finite volume method (FVM) to solve the RANS equations on a three dimensional non-orthogonal grid with a k-ε model for turbulence closure. The initial stage (Olsen and Melaaen, 1993) and the whole process (Olsen and Kjellesvig, 1998) of scour were simulated and the scour pattern was found close to the experimental results.
However, the transient terms in RANS equations were ignored in their simulations and therefore the calculated flow field did not capture the complexities observed in experimental flow field around a model pier. Moreover, Olsen and Melaaen (1993) concluded that the large fluctuations downstream of the cylinder would not affect the development of the scour hole, which was not consistent with recent findings (such as in
Unger and Hager, 2007); although the obtained maximum scour depth by Olsen and
Kjellesvig (1998) was within the range predicted by various empirical formulas, the formulas themselves were found too conservative for practice (Brauid et al., 2009).
Chrisohodies et al. (2003) developed a FVM model to solve the three-dimensional
URANS with a k-ω turbulence closure to study the flow in the vicinity of a typical
- 26 -
abutment geometry with a fixed, flat bed. The result was compared with the experimental
findings and showed good agreement. Large-scale unsteadiness, such as the re-circulating
flow and vortex in the upstream and the separated flow with large-scale eddies, was
successfully simulated. They concluded that the growth of the scour hole was enhanced
by a downward velocity component and the intense turbulent fluctuations in the vicinity
of the scour hole may further contribute to the erosion mechanism and the growth of
scour. Ge et al. (2005), Ge and Sotiropoulos (2005) continued Chrisohodies’ work
(Chrisohodies et al., 2003) and developed a general-purpose numerical method to solve the 3-D URANS. This method was capable of simulating the real-life hydraulic engineering flows containing complex geometries at full-scale Reynolds number. Efforts were made to handle the arbitrarily complex geometries employing domain decomposition with chimera overset grids. The model captured the most experimental trends with good accuracy. However, the calculated distribution of the turbulence kinetic energy was found discrepant with the experimental results. Khosronejad et al. (2011) expanded Ge’s research (Ge et al. 2005) to incorporate the flow-bed interaction. This study highlighted the application of the flow-structure interaction curvilinear immersed boundary (FSI-CURVIB) numerical method of Borazjani et al. (2008) for modeling the flow-bed interaction. Their simulations, to the best of our knowledge, employed the finest numerical resolution so far for coupled hyrdo-morphodynamics simulations of bend flows. The model was further expanded to investigate the scour around bridge piers with different shapes (Khosronejad et al., 2012).
Olsen (2003) introduced a model called Sediment Simulation In Intakes with Multiblock option (SSIIM) to the simulation of water and sediment flows. The SSIIM program
- 27 -
solved the URANS with the k-ε model on a three-dimensional almost general non- orthogonal grid and the sediment transport was modeled with both the suspend load and the bed load. Minor et al. (2007a, 2007b), Esmaeili et al. (2009), Elsaeed (2011) and
Aarabi et al. (2011) employed the SSIIM model to simulate the local scour around bridge piers or barbs. The simulation results were compared with several most famous scour depth prediction formulas and it concluded that SSIIM could be employed to simulate the time dependent scour process around pile groups with low Froude number.
Roulund et al. (2005) simulated the live-bed scour around a circular pier with a flow code,
EllipSys3D, to solve the URANS with a k-ω model for turbulence closure. They resolved the horseshoe vortex and in some cases they also resolved the vortex shedding in the downstream. The simulating procedure in this study was also claimed as a general approach on numerical simulation of scour (Sumer, 2007).
In Zhang et al. (2005, 2006), the URANS was solved with the k-ε model for turbulence closure. A moving unstructured mesh based FVM was adopted and arbitrary polyhedral mesh up to six faces was used in the calculation. Scour process around both the submerged and non-submerged spur dikes were simulated. The vortex structures were resolved and the sediment behavior was reasonably reproduced. However, the unstructured moving mesh method was not applicable if the non-linear k-ε model was employed.
Liu and García (2008) developed a three dimensional code called FOAMSCOUR for local scour with free surface and automatic mesh deformation. This model solved the
URANS with k-ε closure in a FVM scheme while captured the free surface via the
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volume of fluid (VOF) method (an Eulerian approach) and modeled the scour process through the moving mesh method (a Lagrangian approach). It was worth noting that in
this model, two meshes were used: one was for the flow domain which was three
dimensional; and the other was for the “virtual” sediment domain which was two dimensional. The information exchanges between the two meshes were realized through mapping techniques. After the flow model was solved, the parameters such as the shear stresses at the bed surface was mapped to the 2D sediment mesh; the sediment model then calculated the induced bed elevation change using such parameters; the elevation data was then mapped back to the bed of the 3D flow model where it served as the new boundary. Mapping back and forth of the data resulted in loss of accuracy in nature, but the authors claimed that the accuracy was not a problem provided that the meshes were fine enough. The flow field and scour pattern for turbulent wall jet scour and wave scour around a vertical cylinder was simulated and was consistent with the experimental data.
Zhao et al. (2010) developed a finite element method (FEM) numerical model to simulate the local scour around a submerged vertical cylinder. Details of this FEM method can be found in Zhao et al. (2009). The Arbitrary Lagrangian Eulerian (ALE) scheme was employed to solve the URANS with a continuously developing bed boundary. The
URANS was closed with the k-ω SST (shear-stress transport) model. This study quantified the dependence of scour depth on the cylinder height. It was concluded that the decrease of the cylinder height resulted in the weakening of the horseshoe vortex and vortex shedding and thus smaller scour depth. It should be noted that this study focused on the submerged pier and showed the potential of their FEM model for study of scour phenomenon in the sub-sea scenario.
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2.1.2. Large Eddy Simulation (LES) models
LES became a popular technique for turbulent flow simulation in the past decades. The core idea of LES is that the turbulence in different scales is resolved employing different strategies. Different from RANS-based technique which is time averaged, LES is developed from the spatially and temporally filtered/averaged Navier-Stokes equations.
The flow is decomposed into a spatially- averaged part (Eq. 2.8) and a fluctuating part
( ui= uuˆ ii + ′ ). The spatial filtering is achieved by means of filter functions G(ξ, Δ) in Eq.
2.8 where Δ is the filter cutoff width. Eddies whose sizes are greater than the cutoff
width are resolved and those smaller than the cutoff width will be rejected and modeled
using turbulence models. In practice, the cutoff width is often chosen to be of the same
order as the grid size.
After spatial filtering, the Navier-Stokes equations transforms to Eq. 2.9 (the spatially-
averaged quantities are denoted with sign ˆ⋅ ). Different from the Reynolds averaged
approaches which introduce Reynolds stresses tensors, the LES approach brings in a
subgrid stresses tensor, τρij=()uu ij − uuˆˆ ij, which is the main cause of the difficulties to
solve the Navier-Stokes equations in LES.
∞ uGˆ =(,ξ ∆⋅ ) u () ξξd (2.8) ∫−∞
∂uˆi = 0 ∂xi 2 (2.9) ∂∂uuˆˆ11∂pˆ ∂ u ˆ ∂τ ij ii+ufˆ =− +ν i +−ˆ ∂ji ∂ρρ ∂ ∂∂ ∂ t xj x i xx jj xj
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Spatial filtering separates the Navier-Stokes equations to two parts, the “large eddies”
part and the “small eddies” part. The large eddies are resolved directly and thus they can
be captured with high accuracy; similar to the turbulence closure models in RANS and
URANS systems, the small eddies are modeled with certain subgrid-scale models.
The subgrid stresses tensor can be rewritten as in Eq. 2.10.
τρ=−+++ ρ ρ′ ρ ′ ρ ′′ ij( uuˆˆ ij uu i j) ( uuˆ ij uu ij ˆ) uu ij (2.10)
On the right hand side of the expression, the terms in the first and second bracket are the
Leonard stresses and the cross-stresses respectively and these terms can be computed
through approximate methods (Leonard (1974) and Ferziger (1977)). The last term on the
right hand side of Eq. 2.10 is called the LES Reynolds stresses which accounts for the
interactions of the Sub-Grid Scale (SGS) eddies and can be modeled with various SGS
turbulence models.
Common SGS models include the standard Smagorinsky’s subgrid-scale (SGS) model,
the dynamic Smagorinsky’s SGS model, the RNG-LES model, the Wall-adapting local
eddy-viscosity (WALE) model and the Kinetic energy subgrid-scale model. Here only the
general idea of the standard Smagorinsky’s SGS model is presented. For details of other
advanced models, the readers are referred to reviews by Lesieur and Métais (1996) and
Meneveau and Katz (2000).
In the standard Smagorinsky’s SGS model (Smagorinsky, 1963), the subgrid-scale
stresses are related to the strain rate tensor of the resolved fields through an eddy
viscosity νSGS (Eq. 2.11).
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∂uˆ ∂uˆ j 1 τ=−2 ρν i ++τ δ (2.11) ij SGS ∂∂ ii ij xxji3
This model is also a Boussinesq-type model and has the similar formation with Eq. 2.6.
The SGS viscosity in the Smagorinsky’s model has the form of,
∂ ˆ 2 22∂uˆi u j ν SGS =CSGS ∆+ (2.12) 2 ∂∂xxji where CSGS is a constant.
In the dynamic Smagorinsky’s SGS model, a dynamic procedure is developed to calculate the Smagorinsky constant in order to include the influence of sub-scale turbulence on the resolved field (Germano et al., 1991).
In the specific area of bridge scour, the Smagorinsky’s SGS turbulence model is most widely used for a LES model. Tseng et al. (2000) performed LES simulation of the flow past bridge piers. Their model employed a finite volume method based on MacCormack’s explicit predictor–corrector scheme to solve weakly compressible hydrodynamic flow equations, together with Smagorinsky’s SGS turbulence model. Circular and square piers were simulated; and the horseshoe vortex around the pier, the down flow in front of the piers and the wake vortex behind the piers were resolved. The results were in good agreement with experimental finding in Raudkivi and Ettema (1983) and Dargahi (1989).
Although no scour was simulated, the authors argued that the final scour was a result of combined action of bed shear and down flow, reflecting the influence of vortex system.
However, no data was provided on the structure and time evolution of the HV system or on the unsteady wake and their spectral content, except the main wake shedding
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frequency (Kirkil and Constantinescu, 2005). The application of this LES model can also
be found in Chang et al. (2001, 2004).
Dynamic Smagorinsky’s SGS models was also developed and adopted for scour
simulation. Constantinescu and his co-workers (Kirkil and Constantinescu, 2005 and
2007; Kirkil et al., 2008) utilized a massively parallel LES flow solver (Mahesh et al.,
2004), which is a FVM solver using a predictor-corrector formulation on unstructured
grids, to study the HV system around a circular bridge pier located on initial flatbed
(Kirkil and Constantinescu, 2007) and equilibrium scoured bed (Kirkil and
Constantinescu, 2005 and 2007; Kirkil et al., 2008). The dynamic, instead of the standard
(constant coefficient) Smagorinsky’s SGS model was used to account for the subgrid
scale effects; and the logarithmic law of the wall assumption were not employed due to its known deficiencies in the case where the HV regions were dominated by separation and adverse pressure gradients. Their simulations indicated that multiple eddies was
contained in the HV system, which was highly dependent on the azimuthal angle. They
also observed that the legs of the main horseshoe structures were sometimes entrained in
the region behind cylinder and convected downstream; and this phenomenon could
locally increase the bed shear stress beneath them. Detail description about the interaction
between the HV system and the detached shear layers, together with the bed shear stress
corresponding to these phenomena, can be found in Kirkil et al. (2008). The numerically
derived distribution of time-averaged bed-friction velocity around the cylinder was found in good agreement with the equilibrium scour-hole bathymetry measured during the laboratory experiments. Their studies gave valuable insights to the mechanism for sediment entrainment in the regions situated on the two sides of the cylinder. The same
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LES scheme was also employed to study the flow and scour mechanism around isolated
spur dikes in a shallow open channel (Koken and Constantinescu, 2008a and 2008b), the
coherent structures and mass exchange processes in channel flow with two laterally
submerged groynes (McCoy et al., 2005 and 2007), and the flow around submerged
groynes in a sharp bend (Kashyap et al., 2010).
2.1.3. Detached Eddies Simulation (DES) models
As mentioned in Section 2.1.2, LES can capture mean flow characteristics with higher
accuracy than URANS models and can resolve dynamics of the coherent turbulent
structures, while URANS are more capable than LES to deal with in the near wall
turbulence modeling. The so called detached eddy simulation (DES), which is a Hybrid
URANS/LES technique, attempts to combine the merits of URANS and LES.
Due to its strong demand for computational resources, the well-resolving LES methods
used for hydraulic engineering simulations are limited to relatively small Reynolds
number situations (in the order of 104) or laboratory experiment scales. Even with
simplified wall functions for near wall regions in order to reduce the overall
computational cost, it is still not practical to apply LES to real flow past hydraulic structures in a river channel in the foreseeable future (Keylock et al., 2012). The hybrid
URANS/LES methods, on the other hand, resolve the near wall flow structures using a
URANS model and resolve the coherent large scale turbulent flows in the remaining domain. In this way, it does not only ensure the simulation accuracy, but also improved the calculation efficiency in terms of requirement for computational resources. It is practical to apply the hybrid URANS/LES methods, among which the DES is the most
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popular one, to model real life flows past obstructions with Reynolds numbers in the
order of 105 and 106, which are close to the values for the small natural rivers.
The original DES model by Spalart et al. (1997) is built based on the Spalart-Allmaras
(S-A) RANS/URANS model. This DES model keeps the S-A URANS model near the wall and transforms it to the Smagorinsky’s LES model in the remaining domain through a modified distance function:
d≡∆min ( dC, DES 1 ) (2.13)
where d is the distance from the solid wall, CDES is a constant and Δ1 is the largest
dimension of the grid cell.
Other definitions of this length scale criteria ( d ) were developed recently to eliminate
certain potentially very serious deficiencies for practical applications. And these
modifications lead to the so-called Delayed DES (DDES) and the DES with a low-Re
modification (DES-LR). The details can be found in Spalart et al. (2006).
Applications of DES to scour and related hydraulic problems are reviewed in the
following context.
Sotiropoulos and co-workers (Paik et al., 2004; Paik et al., 2007; Paik et al., 2009;
Escauriaza and Sotiropoulos 2011a, 2011b and 2011c) are major players who
investigated the turbulent flow past wall mounted hydraulic structures using the DES
technique. In their applications, several versions of DES (with different length scale to
control the transition between LES and URANS), namely the standard DES (Spalart et al.,
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1997), the adjusted DES (Paik et al., 2007), the Delayed DES (DDES, Spalart et al., 2006)
and the DES with a low-Re modification (DES-LR, Spalart et al., 2006) was employed.
The original version of DES (Spalart et al., 1997) was first employed to evaluate the
potential of using DES methods to capture the complex 3D shear flows in a channel with
obstructions (Paik et al., 2004). This study demonstrated that unsteady statistical turbulence models such as URANS and DES were capable to simulate the obstruction
induced unsteady coherent structures with reasonable accuracy. Additionally, DES
models were superior to URANS models to capture the rich dynamics of such coherent
flow structures.
Paik et al. (2007) proposed an adjusted DES model to alleviate one of the well-known
shortcomings of DES—premature, laminar-like flow separation. A new length scale
based on the measured mean horseshoe vortex core from the wall Hcore was introduced to enforce the presence of a URANS layer regardless of the local grid spacing in order to prevent the interface of URANS and LES region from being situated too close to the wall
(Paik et al., 2007). The simulation captured most experimental trends with good qualitative and quantitative accuracy, and the only remaining discrepancy between the simulations and the experiments lied in the fact that the simulated location of the mean horseshoe vortex core occurred somewhat upstream of the measured location. Based on the simulation results, the mechanism for the onset of the bimodal coherent dynamics was proposed, which may give insight on the mechanism for the sediment transport near these regions. Escauriaza and Sotiropoulos (2011c) employed the adjusted DES model (Paik et al., 2007) to study the Reynolds number effects on the coherent dynamics of the turbulent horseshoe vortex system around circular cylinders.
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Escauriaza and Sotiropoulos (2011a) coupled the adjusted DES model to a new bed load
transport model which directly incorporated the effect of the instantaneous flow field on
sediment transport. This sediment transport model was inspired by an earlier Eulerian-
Lagrangian model (Escauriaza and Sotiropoulos, 2011b) to compute the sediment velocity. With this model, the dynamics of the bed erosion was captured for the first time.
To the best of our knowledge, this is the only model that employed a three-dimensional eddy-resolving CFD method to simulate the initial stage of scour process around an obstruction in an open channel.
Another major DES player on scouring related flow simulation is Constantinescu and co- workers. This group also use the Spalart-Allmaras (S-A) RANS model as the base model in the standard DES (by Spalart et al., 1997). The numerical solver for their model is briefly summarized in Kirkil et al. (2009) and detailed description of the DES code can be found in Constantinescu and Squires (2004). Different from Sotiropoulos’ group who
developed an adjusted DES method, this group overcame the deficiency of the standard
DES models, i.e., the premature, laminar flow separation by using an unsteady fully-
developed inlet boundary condition. This unsteady inlet flow could be obtained using a
separate precursor simulation or just expanding the domain artificially in order to create a
well-developed flow by the time the flow reached the “true” inlet (Keylock et al., 2012).
Studies of the effect of the structure of the inlet flow on the simulated turbulent fields
using eddy-resolving numerical models can be found in Chang et al. (2007) for DES
models and Keylock et al. (2011) for LES models. In Constantinescu’s group, this inflow
condition was obtained from a preliminary LES or DES simulation of the channel flow
which had the identical section to the investigated one with obstructions. With such
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inflow conditions, they not only captured the bimodal oscillations and other flow and
turbulence quantities, but also predicted a more accurate location of the horseshoe system
around the obstructions (Koken and Constantinescu, 2009); with the adjusted DES model
or other gridding adjustment methods, on the other hand, often predicted that the
horseshoe system was located upstream of the experimental data (for example, in Paik et
al. (2007)). All of these studies suggest that a fully developed unsteady inflow condition
which is as close as possible to the realistic flow condition is a prerequisite for
successfully capturing all the features of the flow past an obstacle in an open channel;
and with such treatments, the dependence of DES on the grid (i.e., adjusted DES) and the
need for the correction in DDES is reduced.
Kirkil et al. (2009) employed the above mentioned DES model to study the large-scale
coherent eddies in the flow around a circular pier with an equilibrium scour hole.
Detailed study of the dynamics of the main necklace vortices (NV) of the horseshoe
vortex system was conducted and it was stated that the bimodal large-scale oscillations of
the NV was responsible for the sediment entrainment and transport during the later stages of the scour process; one of the possible mechanisms for sediment removal behind the pier might be the curving of the legs of the NV toward the back of the pier followed
by the detachment of a streak of vortices and its convection away from the pier at a small
distance from the bed (similar to the result from LES simulation (Kirkil et al., 2008).
Kirkil and Constantinescu (2009) utilized the same DES model to investigate the
influence of the shape of the obstacle in stream and found that compared with circular
obstructions, high-aspect-ratio rectangular obstructions resulted in higher shear stress at
large distance from the obstruction and higher pressure fluctuations on the bed.
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Koken and Gogus (2010) investigated effect of abutment length on the bed shear stress
and the horseshoe vortex system by means of DES with the model described in (Kirkil et
al., 2009). Turbulent flow around two abutments with different length was simulated and the results revealed that the pattern of the bed shear stress was similar in both cases while there were some quantitative differences due to the change in the strength of the Necklace
Vortices (NV) and the blockage ratio at the attached bridge cross section. The mean pressure RMS in the long abutment case was approximately two times larger throughout all the amplified regions than that in the short abutment case. Koken and Constantinescu
(2011) studied the flow and turbulence feature in a scour hole around spike dikes and discussed the scour hole development mechanism. Chang et al. (2011) used a DES model developed in Chang et al. (2007), which was almost the same with the model used in
Kirkil et al. (2009), to investigate the vortical structure of the flow at a channel Reynolds number as high as 2.4×105 around a high-aspect-ratio rectangular bridge pier with a small or moderate angle of attack. For small angles of attack (for example, 0º and 15º), the results showed that the horseshoe vortex system played a relatively minor role in the entrainment of sediment from the bed and the amplification effect of the bed friction velocity due to the passage of the roller vortices was relatively small; whereas for a moderate attack angle such as 30º, the bed friction velocity was significantly amplified due to the dynamics of the horseshoe vortex and the roller vortices (Chang et al., 2011).
Scale effects were also investigated using this DES model for flow past circular piers within a scour hole (Kirkil et al., 2009) and for flow past a side wall (or a spur dike) situated on a flat bed or within a scoured bed (Koken and Constantinescu, 2009 and
2011).
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Koken and Constantinescu (2011) compared the performance of different eddy-resolving methods including DES with the SA model as the base model (SA DES), DES with the k-
ω SST model as the base model (SST-DES), and LES with the classical Smagorinsky model and wall functions. It concluded in that the base model for the DES played a relatively minor role. The mean flow and turbulences features predicted by SA DES and
SST DES were very close to each other both inside the upstream part of the scour hole and downstream from the spur dike. It also concluded in that using a simplified wall model in the LES model would deteriorate the performance of the LES method in capturing the strong, large-scale oscillations of the main necklace vortex. By contrast, the well-resolved LES (without wall functions) at low Reynolds numbers and the DES methods using RANS models to resolve the near wall region both can successfully predict such strong bimodal oscillations. These results underscored the importance of the complex wall treatment methods for eddy-resolving methods.
One of the implications of these conclusions is that when expanding small scale laboratory experimental findings to practice applications, the scale effect should be accounted for; another implication is that eddy-resolving methods especially DES methods, which can resolve the rich dynamics of the turbulent structures, are critical in scour research related to high Reynolds number flows, which are hard to simulate in laboratories.
2.2 TWO-PHASE MODELS FOR BRIDGE SCOUR MODELING
Bridge scour involves interactions between different phases, namely, structure, fluid flow and soil particles. Such interactions make bridge scour an extremely complex problem.
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Single-phased models simplify the complex interactions through certain morphologic models, which typically include sediment transportation equations, bed slide estimation and proper morphology adjustments, and mass balance for sediments. Although such
models are sometimes effective to predict the maximum scour depths, the accuracy of the
results are compromised by the empirical or at best semi-empirical nature of the sediment
transportation equations; and besides, they are only marginally valuable for studying the
underlying mechanism of the scour phenomenon.
In recent years, two-phase models are developed to simulate the scour or erosion process.
These models treat the sediment particles as an independent phase. They simultaneously
couple fluid and particle phases and consider the interphasial interactions. Therefore,
two-phase models provide holistic modeling of the scour phenomena and are expected to
be more accurate in scour depth prediction as well as more valuable in understanding the
scour mechanism. Major challenges in two phase models lie in computational
implementations. Different strategies have been attempted. For example, the fluid flow
(liquid phase) and sediment particles (solid phase) can be modeled either in an Eulerian
formulation, a Lagrangian formulation or mix of Eulerian-Lagrangian formulation. This sets the basis for Eulerian-Eulerian models, Eulerian-Lagrangian models, and
Lagrangian-Lagrangian models in bridge scour simulations. This section reviews recent developments of two-phase models for bridge scour simulations.
2.2.1. Eulerian-Eulerian coupling models
Flow can be studied in two distinctive frames of reference, namely, Eulerian and
Lagrangian frames. In an Eulerian specification, the position is determinate and the flow
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quantities at this fixed position are studied; on the other hand, the flow particles or flow parcels are “tracked” in a Lagrangian specification, that is, one defines a particle and follows its path in calculations, whereby the flow quantities are associated with the particles.
The Eulerian-Eulerian couples two phase flow describes both the fluid phase and the solid phase using appropriately modified Navier-Stokes equations; the coupling between the two phases is achieved through momentum transfer terms. Typically, the fluid phase is closed with a turbulence closure while forces such as drag (fluid-solid), lift (fluid-solid), collision (solid-solid), friction (solid-solid) and etc. are used to account for the interactions between phases or in each phase. The equations for the two phases are solved in an Eulerian frame. The Eulerian-Eulerian coupled two phase flow is recently introduced to the area of sediment erosion simulation (Zhao and Fernando, 2007;
Amoudry and Liu, 2009; Liu and Shen, 2010; Azhari et al., 2010; Qian et al., 2010;
Yeganeh-Bakhtiary et al., 2011). The successful implementation of such models shows potentials of applying the Eulerian-Eulerian models to bridge scour simulations.
2.2.2. Eulerian-Lagrangian Models
In the Eulerian-Lagrangian Models, the fluid flow is treated with Eulerian formulation while the particles are described with Lagrangian formulation. Typically, Lagrangian approaches are rarely adopted to study fluid flow since it is very difficult to define and track a fluid particle. However, it is ideal to simulate the movement of sediment particles in fluid using the Lagrangian approach. In a scouring problem, the sediment particles are discrete solids in nature and the interactions between flow and particles can be well
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captured if the particles are treated as solids. This advantage promoted the development of Eulerian-Lagrangian models for bridge scour simulations.
Pasiok and Stilger-Szydlo (2010) coupled a LES model with a discrete solid particle motion model to investigate the turbulence flow around bridge piers and the mechanisms of the transportation of bed material grains. An OpenFOAM CFD toolbox released from
OpenCFD was employed to solve the spatially filtered N-S equations with a dynamic
Smagorinsky SGS model. And the finite volume method (FVM) with collocated, unstructured grids was used. On the other side, the particle motion model was defined based on Newton’s second law, in which friction (Schiller and Nauman formulation, Clift et al., 1978), collision (hard sphere model, Leszczynski, 2005) and gravity was considered in this study. The simulation results indicated that particles moved in a strong jet directed towards the free surface and the jet was enclosed by downstream pier wall and vertical wake vortices. And these results were different from those from the author’s previous studies with zero mass marker-particles (Pasiok et al., 2004). In the latter study, the zero mass marker particles tended to concentrate in vertical vortices cores and once trapped into such vortices, markers were transported out of the scour hole.
Escauriaza et al. (2011b) conducted an interesting numerical experiment to study the bed- load transport in turbulent junction flows. This study proposed a Lagrangian model for sediment particle, coupled with the DES model for junction flows. The Lagrangian model accounted for the bed-particle and particle-fluid coupling, neglecting the particle-particle interactions (i.e., the particles are assumed to be in dilute flow). The simulation illustrated the highly intermittent transport of sediment grains and exhibits essentially all the characteristics of bed-load sediment transport observed in laboratory and field
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experiments. The global bed-load flux was also studied to relate the sediment transport
process with the coherent structures of the flow. These results motivated the development
of new Eulerian bed-load transport models which incorporate the influence of unsteady conditions, which is really encouraging and promising in the authors’ opinion.
2.2.3. Lagrangian-Lagrangian Models
Lagrangian-Lagrangian models treat both the flow and the particles in a Lagrangian
frame. These models typically use mesh-free particle (Lagrangian) methods due to their
capability to simulate boundary-interface deformation and fragmentations. Example particle-based methods include the smoothed particle hydrodynamics (SPH), the discrete
element method (DEM), the moving particle semi-implicit (MPS) methods, the particle
finite element method (PFEM) and the finite volume particle methods (FVPM).
SPH method (Monaghan 1992, 2005), which was a one of the most popular particle
method, was also applied by several researchers to study the flow past bluff bodies
(Shadloo et al., 2011) and to study the erosion problems for Computer Graphic usages
(Krištof et al., 2009) or for pure scour research purposes (Zou, 2007; Sibilla, 2007 and
2008; Mirmohammadi and Ketabdari, 2011; Chen et al., 2011). For scour modeling with
the SPH methods, the sediment transport could be modeled as a fluid phase (typically
non-Newtonian flow) by solving convection-diffusion equations (Zou, 2007;
Mirmohammadi and Ketabdari, 2011; and Sibilla, 2007 and 2008); the sediment particles
could also be modeled using physical-based models as in Eulerian methods, where the
erosion rate was related to the shear stress (Krištof et al., 2009; Chen et al., 2011).
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Some pioneer work on scour or erosion with other particle-based methods were also seen
in recent years. Pan et al. (2010) applied a DEM method to conduct the microscopic
study on soft rock erosion, where the rock material was modeled as granular flow with
inter-particle bonding and the scour was simulated as the process of de-bonding.
Although their work was for the rock erosion, it has potential to be expanded to simulate
the soil erosion problems.
A MPS based model was developed by Shakibaeinia and Jin (2011) to simulate the bed
erosion due to dam break. In their modeling, the solid particles were treated as a non-
Newtonian fluid and the inter-phase forces were originated from density and viscosity difference between particles.
Particle finite element method (PFEM) represents fluids with a Lagrangian formulation and solves the equations using a stabilized FEM approach (Oñate et al., 2008). Such a method was applied to model bed erosion and the onset of erosion was defined and controlled using fraction work originated by the fluid shear stress on the bed surface
(Oñate et al., 2006).
As one can see the potential of applying the Lagrangian-Lagrangian methods to scour problems, one should also notice the main drawbacks of such methods: 1) implementation of sophisticated turbulence models in particle based methods are still lacking; 2) representation of the inlet and outlet boundary conditions which are similar to
the real flow in river channels is a non-trivial problem; 3) for large scale flows with high
Reynolds numbers, the demand on the computational resources for the particle based
methods are enormous.
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2.3. DISCUSSIONS
2.3.1. Comparison of different turbulence modeling strategies
The basic assumptions, advantages and limitations of different CFD approaches (i.e.
RANS, URANS, LES and DES, etc.) have been discussed in each specific Section. The following is a brief discussion that compares the different CFD approaches.
RANS is an efficient engineering modeling tool to simulate steady state flow. It can capture the mean flow characteristics with reasonable accuracy. It, however, cannot resolve any coherent structures as well as the increased turbulence statistics in the vicinity of the junction area, regardless of which type of turbulence closure model (i.e., linear, nonlinear eddy viscosity models, second-moment closure models) is employed.
Due to the transient nature, URANS can simulate large scale organized coherent vortices structures, such as horseshoe vortex and vortex shedding. However only steady vortex systems can be accurately resolved because of the inherent excessive diffusivity of
URANS system even when second moment closure models are used. LES, in principle, is capable of resolving the bimodal structure and the strong unsteady dynamics of the coherent structures in turbulent flow. However the implementations of computational simulations with LES are restricted to flow with small Reynolds numbers, mostly due to constraints in computational power. As a hybrid URANS/LES model, DES can resolve essentially all the energetic turbulence scales produced by the fluctuations in the flow for high Reynolds numbers. Specific attention, however, should be paid to the treatment of the DES length scale and the inflow conditions. Since finer meshes are required by LES
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and DES approaches, the demand on the computational capability increase drastically,
compared with the RANS and URANS models.
Various models exist for the closure of RANS and URANS systems and the RANS part
of the DES formations (Versteeg and Malalasekera, 2007; Launder and Sandham, 2002;
Sotiropoulos, 2005). A general observation and remark on their applications to
simulations of flow and scour around hydraulic structures are summarized here:
(1) The standard k-ε model, in which two transport equations for the turbulence kinetic
energy (k) and the rate of dissipation of the turbulence kinetic energy (ε) are solved, is
widely used for the modeling of flow and scour around hydraulic structures as seen in
Olsen and Melaaen (1993), Olsen and Kjellesvig (1998) and Olsen (2003). This model is
also commonly available in commercial CFD packages and used in bridge scour
simulations as seen in (Ali and Karim, 2002; Liu and García, 2008; and Richardson and
Panchang, 1998). The limitation of the standard k-ε model lies in its isotropic eddy viscosity assumption (Versteeg and Malalasekera, 2007) and its incapability to deal with adverse pressure gradients and flow separation, which are the key characteristics of flow around bridge pier.
(2) The non-linear k-ε models including the renormalization group (RNG) k-ε models are expected to overcome the limitations of standard k-ε models to a certain extent. Such models are capable of studying more complex fluid viscosity schema including flow separation. For example, a non-linear k-ε model was applied by Kimura and Hosoda
(2003) to simulate the scour around spur dikes and cylindrical piers and the model simulation results were validated with laboratory experimental data (Kimura et al., 2004;
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Nagata et al., 2005; and Zhang et al., 2009). This turbulence closure models was proven
to be equivalent to the nonlinear explicit eddy-viscosity model in the algebraic Reynolds-
stress model (by Pope, 1975) and the second order renormalization group (RNG) k-ε
model (by Yakhot and Orszag, 1986). Another non-linear k-ε model was employed to close a steady RANS system to simulate the local scour around a bridge pier (Li, 2004).
The RNG k-ε model was applied by Lu et al. (2005 and 2006) to study the mechanism of local scour around pipelines and the capability of the RNG k-ε model was validated through comparison with the results from a LES model. Huai et al. (2011) also employed the RNG k-ε model to study the vertical jet induced sandy bed erosion.
(3) Other models that extended the standard k-ω models include the Wilcox k-ω models
(Wilcox, 1994) and Menter shear stress transport (SST) k-ω models (Menter, 1992 and
1994), where the turbulence frequency ω instead of turbulence dissipation rate ε is used
as the second variable. Examples are the bridge scour simulations by Chrisohodies et al.
(2003) and Roulund et al. (2005) using the Wilcox k-ω model and by Zhao and Cheng
(2010) using the SST k-ω models. All of these models leaded to successful reproduction
of recirculating vortex and separating flow in the wake.
(4) Another category of extended k-ω model is the Spalart-Allmaras (S-A) models
(Spalart and Allmaras, 1994), which is a one-equitation model suitable for adverse
pressure gradients flows. The S-A models were employed by Frana (2008) and Kirkil et
al. (2009) for modeling of scour phenomena.
(5) Reynolds stress equation models (RSM) is the most complex turbulence model (by
Launder et al. 1975), where the exact Reynolds stress transportation equations are used. It
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requires much more computational resources than the other turbulence models. RSM
models are included in some commercial packages such as in FLUENT® and were applied by Petel and Gill (2006) to study the curved channel flows and by Salaheldin et al.
(2004) to calculate the surface level around bridge pier. The results obtained by several
turbulence models were compared to experimental data and the RSM model was proven
to produce the best results.
In the authors’ opinion, considering the advantages and deficiencies of each strategy and
the available computational resources, DES is the most efficient approach to simulate the
scour process around bridge foundations in real life. But this trend is just beginning and
only a few pioneer studies exist in current literatures (e.g., the studies by Escauriaza and
Sotiropoulos, 2011a and 2011b).
2.3.2. Methods for discretization and gridding
Although turbulence modeling is a critical component in the implementation of CFD scour simulation, it is not the only challenge. The formulations for most of the turbulence models can be presented on a single page. But, numerical implementation challenges such as the computing cost and the solution quality are much more difficult to be clearly defined.
Regardless of modeling strategies, the governing equations need to be discretized for numerical solution. Different discretization methods are available for CFD modeling; and the most prevailing ones are the finite difference method, finite volume method, and the
finite element method. There is no method that is absolutely superior to the other
methods since each method has its strengths as well as weaknesses. As their names
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indicate, the finite difference method approximate the derivatives in the governing
equations with finite difference formulations; the finite volume method discretizes the
whole fluid domain into finite volumes and the partial differential equations (PDEs) are
solved at the centroid nodes of the finite volumes; the finite element method meshes the
fluid domain into finite elements and solve the PDEs at nodes on each corner of the finite
element for linear basis and also on nodes between corners for higher order basis.
Traditionally, FDM and FVM dominates the area of the CFD modeling due to their easy
formulation and high computational efficiency; comparatively, the formulations for FEM
methods are much more complicated and they are more demanding on computational
resource. Another reason for the popularity of the FVM is that it ensures the physical
conservation rules at each control volume, whereas it is difficult for FEM methods to satisfy mass conservation and to prevent pressure oscillations. Both FEM and FVM methods accommodates complex geometries and unstructured meshes whilst structured mesh is prerequisite for FDM method, in which the curved meshes have to be converted into orthogonal Cartesian coordinates (Chung, 2010).
Most of the current CFD modeling for bridge scour is based on the FVM discretization.
For example, the commercial CFD packages such as FLUENT® (Ali and Karim, 2002;
Huang et al., 2009; and etc.), and Star-CD® (Kostic et al., 2009; Patil et al., 2009; and etc.)
all applied FVM method; some individually developed solvers such as those by Olsen
and Melaaen (1993), Chrisohodies et al. (2003), Kirkil and Constantinescu (2005) and etc.
also utilized FVM to discretize the PDE equations. FDM is also applied to model the
scour problems, such as those using FLOW3D® (Richardson and Pangchang, 1998; Choi
and Yang, 2002; and etc.). The recent developments of FEM also expanded its
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application to erosion modeling. Examples of pioneer studies utilizing FEM include (Jia
et al., 2001; Zhao et al., 2004; Chen, 2006; Zhao et al., 2006; Vasquez et al., 2008; Zhao
and Cheng, 2010; and Frana, 2008).
Gridding technology is also a vital component for the accuracy and efficiency of the
numerical simulations. Three types of grid are commonly used for bridge scour
simulations, i.e., single-block structured grid, multi-block patch grid, and unstructured
grid.
(1) Single-block structured grid techniques are easy to apply on simple shaped domain. In
the early efforts on three dimensional scour simulations, single-block structured mesh
dominated. These include for example, the simulations in Olsen and Melaaen (1993),
Olsen and Kjellevig (1998) and Richardson and Pangchang (1998). Such gridding method can also be also found in Constantinescu and Patel (1998) and Neary et al. (1999).
However, single-block structured grid techniques are limited to simple geometries because describing a complex domain with a single set of curvilinear coordinates often presents a formidable if not impossible task (Ge et al., 2005). (2) Multi-block approaches with patch grids at interfaces were developed to handle complex geometries. For scour problems, the simulations by researchers (Smith and Foster, 2005 and 2007; Hatton et al.,
2007; Brethour, 2001; and Roulund et al., 2005; and etc.) employed the multi-block gridding approaches. Sinha et al. (1998) employed a multiblock, structured-grid approach to simulate flows in natural river reaches with islands and a patched multiblock approach was used to handle the presence of the islands. The use of multi-block grid techniques improved the capability of CFD to handle complex geometry. (3) Unstructured grids provide flexible gridding in complex 3D domains (Ge et al., 2005). Their applicability to
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steady hydraulic engineering flows and the general numerical formulation applicable for
arbitrarily shaped cells was demonstrated by Lai et al. (2003). The unstructured approach
was employed by recent studies (i.e. Olsen, 2003; Rameshwaran and Naden, 2003; Liu et
al., 2008; Kirkil et al., 2008; Koken and Constantinescu, 2008a and 2008b) to discretize
the complex geometries involved in scour related problems.
Meshing sizes are also vital for successful CFD simulations. In general, eddy-resolving
methods such as LES and DES require much finer meshes than RANS or URANS
models to resolve the rich dynamics of turbulent structures especially in the wall regions
and junctions regions where the flow separation or strong adverse flow exists. Keylock et
al. (2012) made suggestions regarding the meshing in eddy-resolving methods in a geomorphyic context. The first grid surface off the wall boundaries are recommended to be situated at less than 4 wall units for wall-resolving methods; this distance are recommended to be about 30-300 wall units if wall functions are employed. In the bed normal direction, the mesh can be extended to the free surface such that the mesh size in this direction can attain to about 1/20 of the channel depth close to the free surface; and in the horizontal directions, the mesh size can be larger. It is also worth noting that the meshing requirement for well-resolved LES and for a DES to obtain equivalent accuracy is not the same because in the DES the thin attached boundary layer are resolved using
RANS. Therefore, DES is expected to require much less computational resources than
LES for simulating flows with high Reynolds numbers. This is also the main reason that
the DES models are very popular.
2.3.3. Treatment of Boundary conditions
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Setting the proper boundary conditions are also important for the application of numerical
computational methods. Besides the flow-bed interfaces (Eulerian methods) or the flow-
particle interfaces (Lagrangian methods), the boundaries involved in scour modeling also
include boundaries such as the inlet and outlet boundaries, the free surface, the flow-
structure interface, etc. The inlet boundaries are treated as steady free-stream flow in
most Eulerian methods. More advanced models apply fully developed turbulent flow as
the inlet boundary to simulate the real flow (such as in Ge et al. 2005, Ge and
Sotiropoulos 2005). This inlet condition is particularly important for eddy-resolving
methods to obtain high accuracy in areas such as the front of the obstructions in flow
channel (see Section 2.1.3). The free surfaces are mostly treated as rigid lid and
symmetry boundaries to simplify the simulation. However, one should note that this
treatment is only applicable to flows with small Froude number ( Fr= V gD ) because in
such situations the deformations of the free surface close to the obstructions are not
significant. If the Froude number of the flow is high, or if the flow is in flood or wave
conditions, the influence of the free-surface should be considered. For example, in some models the air-water free surface was captured using methods such as volume of fluid
(VOF) (for example, models using Flow-3D®).
2.3.4. Modeling of sediment transport and erosion
Besides the challenges in the flow domain discussed previously, modeling of sediments
and erosion is another critical aspect for reliable scour simulations.
In the single-phase flow methods, the movement of sediment particles are not modeled as a separate “phase”, or, not defined by its own governing equations. Instead, they are
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coupled to the flow domain through certain assumptions (i.e., sediment transport rate
versus average interface shear stress or flow speed) and the river bed profile is updated at
each time step. In Section 2.1, the single-phase methods are categorized based on the
turbulence modeling strategies to emphasize the importance of turbulence. Noteworthily,
the single-phase methods can also be categorized based on the coupling methods between
the flow and the sediment particles, which is briefly described in the following.
The most common approach to couple the flow and sediment erosion is through sediment
transport equations. The sediment transport is often divided into bed load and suspended
load. The bed load are commonly described using empirical or semi-empirical equations
(for summary of various bed load transport equations, the readers are referred to Apsley
and Stansby, 2008; Ouriemi et al., 2009). The suspended load transport is often expressed
as convention-diffusion equations. Most of the bed load models are developed for river
bed erosion research and the bed load transport of sediment is quantified by the so called
bed-load flux, often determined by the local bed shear stress. For scour in sandy
sediments, the bed elevation is updated based on the mass continuity of the sediments and sand slide is monitored by calculating the repose slope of the bed. The final shape of the
scour hole is controlled either by equilibrium shear stress (a representative example for
this approach is detailed in Roulund et al., 2005) or critical velocity.
To simulate scour around hydraulic structure, there are a few commonly used bed-load transport equations such as (1) Meyer-Peter & Muller equations (1948) (used, for example, by Onda et al. (2008), Guven and Gunal (2010) and etc.); (2) Engelund &
Fredsøe equations (1976) (used, for example, by Liang and Cheng (2005), Roulund et al.
(2005), Liu and García (2008), Zhao et al. (2010), Nakamura et al. (2011) and Huai et al.
- 54 -
(2011)), and (3) van Rijn equations (1987) (used for example by Liang et al. (2005),
Zeng et al. (2010), Zhang and Duan (2011)). These traditional bed load transport
equations are typically based on laminate flow assumptions (using the concept of critical
shear stress or critical flow velocity) and uses equilibrium assumptions for the sediment
transport. New equations were also developed to consider the effect of turbulence (Li,
2004; Abbasnia and Ghiassi, 2011) or the instantaneous flow field (Escauriaza and
Sotiropoulos, 2011a). The suspended load transport is sometimes not included in the
sediment modeling since it does not have significant influence on the equilibrium scour
depth for clear-water scour situations (Melville and Sutherland, 1988; Sumer and Fredsøe,
2002). However, it does influence the time-varying evolution of the scour hole. The
suspended load transport is often expressed as convention-diffusion equations and was
incorporated in many simulations such as in (Neyshabouri et al., 2003; Liang et al., 2005;
Liu and García, 2008; Zhao and Cheng, 2008; Zeng et al., 2010; Zhao et al., 2010).
Besides the equilibrium sediment transport equations, sediment transport can also be
modeled in approaches where the pickup, transport and deposition processes are
considered (Nagata et al., 2005; Onda et al., 2008). In the non-equilibrium approaches,
the effect of non-equilibrium sediment transport is considered.
Other alternative methods to model the soil erosion around hydraulic structures are based
on mathematical models and physics-based models. Guven and Gunal (2010) proposed a hybrid model for simulation of scour and flow patterns. Instead of sediment transport equations, this model incorporated a mathematical module which calculated the shape of the developing scour hole. This shape was calculated using an integro-parabolic equation, which was derived from solid discharge and sediment property (porosity). The final
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equilibrium scour shape could also be obtained based on the assumption that the
equilibrium shear stress on the bed was equal to either the critical shear stress of the
sediment (clear-water scour) or the undisturbed bed shear stress (live-bed scour) (Li and
Cheng, 2001). In this way, the scour hole shape could be simulated without using any sediment transport equations. Cunninghame and Armitage (2006) simulated scour and
deposition using the unit stream power method, in which the incipience and development
of the scour was governed by the critical stream power.
Two-phase models treat the sediment particles as a separate phase either as continuum
(Eulerian methods) or as discrete medium (Lagrangian methods). In Eulerian methods,
the movement of the sediment particles is also governed by N-S equations, and the
interaction with fluid is realized through momentum transfer terms. Therefore transport
equations are no longer required. In the Lagrangian method, on the other hand, the
particles are treated as discrete solids and the particles and the fluid are coupled through
multi-way coupling schemes. The obvious advantage of the two-phase flow models is
that the sediment transport formula, which are based on the critical shear stress theory
and used in single-phase methods are not required anymore. Furthermore, Lagrangian
methods can also be employed as a tool to study the underlying mechanism of the souring
phenomenon (Escauriaza and Sotiropoulos, 2011b; Pasiok and Stilger-Szydlo, 2010), or,
to establish a new sediment transport model which incorporate the influence of
turbulence and large-scale coherent structures for the single-phase approaches
(Escauriaza and Sotiropoulos 2011b). Despite the advantages of two-phase flow models,
they also have limitations. For example, the Eulerian methods are more suitable for
sediment transport problems where the sediment is relatively dense; although Lagrangian
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method is favorable for study the mechanism of scour, it may not be ready in current
stage for industrial flow or real-life scouring problems due to its high demand for
computational resources.
2.4. SUMMARY AND CONCLUSIONS
This chapter reviews the CFD model for flow and scour around bridge pier and similar hydraulic structures.
• Different approaches for computational simulations are categorized based on how
they simulate sediment transport and how they simulate turbulence, two major
challenges for bridge scour simulations. Based on how the sediment phase is
treated, the simulation methods are categorized into single-phase flow models,
where the scour is related and coupled to the flow characteristics, and two-phase
flow models, where the sediment particles are modeled as a separate phase. The
single-phase models are future reviewed based on different turbulence modeling
strategies, namely, RANS, URANS, LES and DES. These methods differ in the
resolution of the resolved turbulence scales. The two-phase models are classified
to either Eulerian models or Lagrangian models based on how the sediment
particles are modeled.
• Through the comprehensive review and comparison of different numerical
methods, it is realized that a wealthy number of numerical modeling approaches
are available for simulation of flow and scour around hydraulic structures. Each
method has its own advantages and limitations. In the general sense, there is no
“perfect” method which is superior to all other ones. Computational simulation of
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the scour problem is a very challenging task. The decision on which strategy to be undertook should only be based on factors such as the purpose of the simulation
(industrial application or academic science exploration), what accuracy is required, and availability of computational resources, etc. The methods surveyed in this paper are not exhaustive as new numerical methods continue to emerge that potentially offer higher modeling capabilities with reduced computational power requirements. In our opinions, efforts in such topics are demanding but worthwhile, as they will lead to advancement of science and engineering for bridge scour, a major factor determining the safety of bridges.
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CHAPTER 3
CFD MODELING OF EFFECTS OF PIER CONFIGURATIONS
ON THE FLOW PATTERN AND SCOUR
3.1. INTRODUCTION
It is widely accepted that the vortex structures around the bridge piers (the horseshoe vortex and the lee-wake vortices) will enhance the scour process and they are the main reason for local bridge scour. Besides, a downward flow will form in front of the bridge pier due to reverse pressure; and the downward flow is also assumed to affect the scour process (Ge et al., 2005a,b). It is straightforward to expect that these flow structures will alter significantly for piers with different geometries, thus leading to different scour patterns.
The effect of pier geometry on the local scour patterns has been investigated experimentally (e.g. Dey and Raikar, 2007; Raikar and Dey, 2008; Debnath and
Chaudhuri, 2012; Khosronejad et al., 2012). Researchers are most interested in the prediction of the maximum scour depth; and various empirical equations have been developed to predict the maximum scour depth based on experimental results and dimensional analysis (Arneson et al. 2012, Melville and Stherland, 1988; Debnath and
Chaudhuri, 2012). In these equations, the influence of the shape of the bridge piers on the maximum scour depth is often considered by introducing correction factors (Arneson et
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al. 2012). However, the flow patterns around piers with different geometries have been
seldom symmetrically studied experimentally due to the limitation of the measurement
techniques. Advanced flow sensing techniques such as ADV and PIV are typically
limited for measurement of certain points or planes. It is extremely challenging, if not
impossible, to measure all the points in the 3D space around bridge piers with currently
available techniques. CFD provides an alternative approach to address this challenge.
Flow and scour patterns around circular piers have been extensively studied using CFD
methods in the past decades (see Chapter 2). However, this technique has not been widely applied to study the effect of other pier geometries on the flow characteristics and corresponding scour patterns. Examples include: Tseng et al. (2000) compared the three dimensional flow around square and circular piers using a Large Eddy Simulation (LES)
model; Kirkil and Constantinescu (2009, 2010) studied the flow characteristics around a
high-aspect-ratio rectangular pier (plate) using a Detached Eddy Simulation (DES) model
and the flow patterns were also compared to those around a circular pier; Chang et al.
(2011) evaluated the effect of attack angle on the coherent structure dynamics around a
high-aspect-ratio rectangular cylinder using a DES model and the studied attack angle
was limited to low and moderate angles (i.e., 0°, 15° and 30°).
Although isolated studies exist in the literature, there is no systematic study on the effect
of all the common pier configurations (i.e., pier shape, pier aspect ratio, attack angle) on
the flow patterns. A possible reason is that the CFD models used in previously mentioned
studies are computationally expensive and time consuming; furthermore, most of the
codes are developed by individual researchers and not ready for use by others. Since the
flow pattern around bridge piers is prerequisite to study the mechanism of local scour and
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is critical for countermeasure design and risk management, it is necessary to conduct a
systematic numerical experiment to study the effect of pier configurations on the flow
and scour patterns. To provide a comparison basis, the numerical experiment should be
conducted in such a way that all the conditions rather than the geometries of the piers are
the same. These conditions include the same pier width (thus the same Reynolds number),
the same boundary conditions (inflow and outflow conditions, bed condition, free surface
condition and treatment of the pier surface), the same turbulence modeling strategy, and
the same meshing technique and meshing quality. The turbulence modeling technique
should be both capable to capture the main turbulent vortex structures and
computationally cost-effective thus approachable to practitioners in a wider range.
In this Chapter, the 3D flow fields around piers with different cross-sectional shapes,
aspect ratios and attack angles are simulated with a Reynolds Averaged Navier-Stokes
(RANS) model closed with a k-ω model. The effects of such factors on altering the flow pattern around the pier are systemically evaluated. Specifically, the vortex structures, the downflow in front of the piers and the bed shear stress patterns are qualitatively compared and analyzed. The effect of attack angle, which is the most significant factor among these three, is quantitatively evaluated and a new equation is proposed to estimate the maximum bed shear stress considering the effect of both attack angle and aspect ratio.
Furthermore, the typical scour patterns for piers with different configurations are related and compared to the flow patterns and the bed shear stress patterns; and such analysis provides insights into the scour mechanism and future directions for numerical simulation for scour process around bridge piers. The practical significance of the findings in this study is also underscored.
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In order to model the scour process, the flow model is needed to be coupled with other
models, which defined the changing of the bed morphology. In the end of the Chapter, a
framework is proposed to model the scour process focusing on the modification of the
sediment transport models.
3.2. NUMERICAL METHODS AND VERIFICATION
The flow domain was simulated by the Reynolds Averaged Navier-Stokes (RANS)
equations (Eq. 2.1). Comparison between different closure strategies is made in Chapter
2. In this Chapter, the well-established k-ω model is selected as a compromise between calculation cost and accuracy. The k-ω model is superior to predict the adverse pressure gradient flow which is a main feature in the bridge pier flow compared to the k-ε model; at the mean time it is much cost effective compared to the non-linear turbulence models or the more advanced Reynolds Stress Model (RSM). For the modified k-ω model, k is the turbulence kinetic energy and ω is the specific dissipation rate and the kinetic eddy viscosity can be described as,
k ν = (3.1) t ω
The additional transport equations for the kinetic energy k and specific dissipation rate ω are:
∂k ** ρ+ ρu ⋅∇kP =kT −ρβ k ω +∇⋅(( µ + σ µ ) ∇k) ∂t (3.2) ∂ωω ρ+ ρu ⋅∇ ω = αP − ρβ*2 ω +∇⋅(( µ + σµ) ∇ ω) ∂tkkT
- 62 -
T 222 In Eq. 3.2, the production term PTk =µρ ∇uu: ∇ +( ∇ u) −( ∇⋅ u) −k ∇⋅ u and the ( ) 33
coefficients in Eq. 3.2 are as follows (Wilcox, 2004),
13 1 α=, ββ =ff, β** = β0* , σσ = = 25 0 ββ2
13 1+ 70χω ΩΩij ikS ki βχ0 =, fβω = , = * 3 125 1+ 80χω (βω0 )
10χk ≤ * 91 2 β=, fkβ * = 1+ 680χ , χω=( ∇ ⋅∇ ) 0 100 k χ > 0 k ω + χ 2 k 1 400 k
11∂∂uu∂∂uujj Ω=ii − , S = + ij ∂∂ ij ∂∂ 22xxji xxji
It is worth noting that one of the limitations of RANS models is that it is based on the
linear eddy viscosity and isotropic turbulence assumptions. More advanced turbulence
models such as large eddy simulations (LES), hybrid LES-URANS models or detached eddy simulations (DES) can handle the non-isotropic characteristics of the turbulent flow around obstructs in waterway. However, the computation cost is much more expensive than the RANS models.
In this study, the RANS equations are solved using COMSOL® with stabilized finite
element formulations in combination with damped Newton method. The flow variables
(u, p, k and ω) are grouped to two segregated steps: step1 includes the velocity
components and pressure component and step 2 includes the turbulence kinetic energy
and the specific dissipation rate. Each step is solved using GMRES iterative solvers. The
flow model was validated by simulating the experiment of the flow around bridge pier by
Dargahi (Dargahi 1989). In Dargahi’s experiment, the flow around a cylinder was
visualized; the velocity, pressure and shear stress were measured and were well
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documented and thus it is a good reference for flow model validation. In his experiment,
a cylinder was vertically mounted in a channel flume. The cylinder is 0.15m in diameter
(Dp); the flume is 1.5m in width (W), 19.8m-long and the water is 0.2m in depth (H). The
cylinder is located 18m downstream of the inlet, where the mean velocity is 0.26m/s
corresponding to a cylinder Reynolds number of 3.9×104.
In this numerical model, steady solution of the flow is obtained using the geometry as the same as in Dargahi’s experiment. To reduce the computational cost, the flume was divided to two different separated sections: the first section is 17m long and this part is used to get the fully developed turbulent flow at the outlet boundary; the second section is 2.8m long and the cylinder is placed 1m downstream of the inlet boundary.
The bottom and side walls of the flume and the surface of the cylinder are set as wall and
the boundary condition is the standard wall functions (Kuzmi et al. 2007) (also see Eq.
3.1). The free surface of the water domain is set as slip wall and the symmetry conditions
are employed. The normal velocity at the inlet of the first section of the flume is set as
0.26m/s, which is the mean free stream velocity in the experiments of Dargahi (Dargahi
1989). At the inlet of the second section of the flume, the value of flow variables (u, p, k
and ω) are obtained from the outlet boundary of the first section of the flume. At the
outlet boundaries of both the two flume sections, zero pressure condition is applied.
In Dargahi’s experiment, the measurements were mainly in the region near the cylinder.
This is because rich turbulent structures such as horseshoe vortex and lee-wake vortex are developed in that region and a typical scour hole is also located in the same region.
- 64 -
Therefore, a hollow cylinder region is meshed with very fine meshes to capture the rich turbulent (Figure 3.1).
Figure 3.1. The meshing elements of the computation domain: the white region is the pier; the red region is
the fine mesh zone.
The center of the fine mesh region is at the pier center and the inner and outer diameter is
Dp and 3Dp, respectively. Structured meshes (8 layers) for quadrilateral elements are chosen on the bottom surface (bed) of the flume and the surface of the cylinder for better resolution on the boundary layers, whereas unstructured meshes for tetrahedral elements are chosen at the remaining regions. The maximum and minimum meshing size is
0.0126m and 8.22×10-4m for the fine mesh region, respectively. For the remaining region, the mesh is coarser (maximum and minimum meshing size of 0.029m and 5.48×10-3, respectively). The pier domain, which is a circular cylinder in this case, is blanked in the simulation. More than 1 million mesh elements are generated in total. The meshing elements of the computational domain are shown in Figure 3.1.
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The down flow and the horseshoe vortex are successfully modeled in front of the pier.
Figure 3.2 shows the modeled flow field in the symmetry plane. It shows a clear vortex in
the region between 0.86Dp and 0.66Dp from the pier center. And the vertical position of the vortex is between the bed surface and 0.075H away from the bed.
Figure 3.2. The streamlines and velocity vectors upstream of the cylinder.
The lee-wake vortexes are also resolved (Figure 3.3). Figure 3.3 shows the streamlines
(black) and the velocity vectors (red) on the horizontal plane at different vertical
locations (only the fine mesh zone is included). As seen, at the location of 0.5H from the
bed, the complex lee wake is developed and the horseshoe vortex vanished; at the
location of 0.005H from the bed, however, the horseshoe vortex is observed while the lee
wake vertex degenerates to simple separated flows. These findings reveal the three
dimensional complex structures of the turbulent flow around the pier.
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Figure 3.3. Streamlines and velocity vectors on the horizontal planes at different vertical locations. (a)
z=0.5H; (b) z=0.005H (distances are measured up from the bed)
Parameters such as pressure and bed shear stress are quantitatively evaluated and compared to Dargahi’s measurements. The pressure distributions along the upstream stagnation line on the cylinder and along the symmetry line on the bed are plotted in
Figure 3.4. The pressures along the stagnation line on the cylinder are normalized with the pressure at the top of the line and the pressures along the symmetry line on the bed are normalized with the pressure at the lowest point on the upstream stagnation line.
Figure 3.4 shows the agreement between the calculated results with the measurements is good. And the main trend of the distributions of pressure can be captured using with acceptable accuracy. The pressure gradient along the stagnation line (Figure 3.4a) drives the flow to travel downward and a local boundary layer separation results in the corner vortex (Figure. 3.2). The pressures along the symmetry line on the bed (Figure. 4b) keep as almost a constant between -0.85Dp~-0.65Dp, this plateau, according to Dagahi (1989), is the result of the smoothing effect of the horseshoe vortex. Although there is a discrepancy between the modeled results and the measurements, the locations of the
- 67 -
plateau is predicted with considerable accuracy. This location of the plateau also corresponds to the location of the horseshoe vortex as shown in Figure 3.2.
(a)
(b)
Figure 3.4. Pressure distributions along (a) the upstream stagnation line and (b) the symmetry line on the
bed.
- 68 -
The shear stress distribution on the symmetry line upstream the cylinder is also compared with the measurements using Preston tube (Figure. 3.5). The shear stresses are normalized with the mean shear stress at probe station -2.5Dp away from the cylinder
(Dargahi 1989). From Figure 3.5, it is clear that near the upstream face of the pier, the shear stresses are negative, which means the shear force is oriented oppose to the “x” direction and this is caused by the reverse flow in this region. It can be concluded that the pressure and shear stress calculated with the numerical model correspond to the measured data well. The discrepancies may be attributed to the own limitations of the turbulence model as well as to the uncertainty of the measurement (which is about 3-6% reported by
Dargahi (1989)).
From the comparisons between the numerical and experimental results, the capability of the flow model is validated. And this flow model can be employed in the future simulation of the flow field around piers with great confidence.
Figure 3.5. The mean bed shear stress along the symmetry line upstream of the cylinder.
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3.3. SIMULATION CASES AND COMPUTATIONAL DETAILS
Three groups of simulations were carried out to study the effect of pier shape, aspect ratio
and attack angle, respectively. The fundamental parameters for the simulations cases are
listed in Table 1. Briefly, four cross-sectional shapes are simulated for the pier shape effect, namely, circular, square, diamond, and lenticular; four aspect ratios, namely
L/B=1, 2, 5, 7 (where L is the streamwise length and the B is the width of the pier) were simulated for both piers with rectangular nose and round nose; the angle effects are analyzed for round nosed oblong pier with aspect ratios L/B=2 and L/B=4 at attack angles from 0° to 90° with steps of 15°; a test case for rectangular nosed pier with aspect ratio of 4 at attack angle of 45° is also conducted for verifying and comparison purpose.
Table 3.1. Details for the Test Cases
Diameter D Cross-sectional Aspect Ratio Attack angle Test Cases or Width B shape or nose shape L/B (°) (m)
Circular 0.15 1 0
Square 0.15 1 0 Group 1 Diamond 0.15 1 0
Lenticular 0.15 2 0
Rectangular 0.15 1, 2, 5, 7 0 Group 2 Round 0.15 1, 2, 5, 7 0
Round 0.15 2, 4 (0:15:90) Group 3 Rectangular 0.15 4 45
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The height of the piers, the geometry of the flume, the inlet and outlet conditions, the
wall boundaries and free surface boundaries are all as the same as in the verification case
(Dargahi’s experiment) presented in the former section. In addition, for each test case, the
zone near the pier (typically 2Dp or 2B away from the pier) is meshed with finer
elements and the other areas are meshed with a coarse mesh. The meshing methods and
the overall meshing qualities for all the cases are carefully controlled to eliminate the
influence of meshing sizes.
When studying scour phenomenon, the bed shear stress is an important parameter, which
can be derived from the wall function. The wall function used in this work is modified
from the formulation of Kuzmin et al. (2007) for k-ω turbulence model. In this formulation, the friction velocity can be related to the tangential velocity with Eq. 3.3.
y** yy≤ u + ++ t = 1 * (3.3) u f log y++>β0 yy ++ κ
22 In Eq. 3.3, ut is the tangential velocity ( ut= uu xy + , where ux and uy are the streamwise
and transverse velocity); κ is the Karaman constant with the value of 0.41; y+ is the local
uy Reynolds number defined as y = f , where y is the distance from the wall boundary; + ν
* y+ is a constant (11.06 in this framework); β0 is a constant with value of 5.2 for smooth
walls.
2 The bed shear stress is then calculated as τubf= ρ . The critical shear stress is determined
by a widely used prediction formulae developed by Soulsby (Soulsby, 1997).
**0.30 τ crit = +0.055 1 −− exp( 0.020d ) (3.4) 1+ 1.2d *
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In Eq. 3.4, the non-dimensional bed shear stress and particle diameter is defined as
13 * τ * (sg−1) τ = b and dd= , respectively; the subscript “crit” indicates the ρ (s−1) gd ν 2
critical shear stress. And ρ, s, g, d is the density of the flow, the specific gravity of the sediment particle, the gravity constant and the diameter of the particle, respectively. For sediment particles with specific gravity (s) of 2.7 and diameter of 0.4mm, the calculated critical bed shear stress is 0.22Pa.
3.4. EFFECT OF PIER SHAPE
As previously illustrated, the CFD model is capable to simulate the complex 3D large
scale vortex structures around a circular cylinder. In this section, the effect of the pier
shape of the piers on the three dimensional flow fields is analyzed, including the
comparisons of the vortex structures, tangential and vertical velocity distributions, and
bed shear stresses.
Figure 3.6. Limited streamlines around piers with cross-sectional shapes of circular (a), square (b),
diamond (c) and lenticular.
3.4.1. Vortex structure
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(a)
(b)
Figure 3.7. Vertical velocity distributions along the symmetry line in front of the pier (a) and along the
transverse cut line near the bed in front of the pier (b).
For the square case, the lee-wake vortex is developed further to 7B away from the downstream edge of the pier. This range is fairly larger than the other cases (Figure 3.6).
Furthermore, it can be observed that a pair of side wall vortexes along the two side wall sweeps downstream. And if the bed is erodible, such vortexes can enhance the transport of the sediment particles. The structures of the lee-wake vortex for the circular case and
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the lenticular case are much more complicated than for the square and diamond case. For the former cases, the axes of such vortexes are both perpendicular and parallel to the bed; for the latter cases, the axis of the vortex is mainly parallel to the bed surface.
3.4.2 Vertical velocity
Due to the different shapes of the pier nose, the flow patterns in front of the piers also differ from each other. For the circular and square case, the front surface is blunt, and the flow will experience huge pressure difference when approaching. Therefore, a downflow forms in front of the pier and at the same time flow separates from the side edges. For the diamond case and the lenticular case with sharp front edges, the downflow is much weaker and the flow pattern is mainly dominated by separation of the shear layers. The vertical component of the flow velocity in front of the piers is plotted in Figure 3.7. On the symmetry line on the bed, the magnitude of the downflow decrease with the distance from the pier edge (Figure 3.7(a)) and it decreases fastest for the diamond and lenticular case, which means the downflow only exists on a very small region in front of the piers; on the transverse direction (measured at 0.01B away from the leading edge of the piers), the downflow also decrease as the distance away from the symmetry line and it is clear that the downflow region for the square case and the circular case is much larger than that for the diamond and lenticular case.
Such a downflow should be accompanied by a horizontal flow along the bed directed away from the pier front to satisfy continuity (Ge and Sotiropoulos, 2005a,b). For example, Figure 3.3b showed the streamlines around the circular pier on the bed and it is clear that in the downflow region shown in Figure 3.7, there is horizontal flow away from
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the pier. It is reasonable to expect that this horizontal flow may sweep the bed material away from the pier and induce scour.
3.4.3 Shear stress
Figure 3.8. Contour of the normalized bed shear stress near the piers with different shapes.
The bed shear stress calculated from the numerical model is normalized with the
calculated critical bed shear stress (τcrit). The contour of the normalized bed shear stress
τ (τ ' = ) in the near pier region (a circle with diameter of 3B) are plotted in Figure 3.8. τ crit
The contour line with value of 1 (area enclosed within this line is considered as the scour
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critical region) is highlighted. Since the bed shear stress is related to the tangential velocity through Eq. 3.3, this figure is also an indicator of the distribution pattern of the tangential velocity.
It can be observed that the patterns of the critical region of these test cases are obviously different and are related to the separated shear layers around the piers. For the square and diamond case, the shear layers are almost shed away from the two sharp corners with angles around 45° to the streamwise symmetry plane and the maximum shear stress is found to be located close to the side corners, too; for the circular case, the shedding angle is similar and the maximum shear stress is located at around 40° from the symmetry line; for the lenticular case, due to the combination of a sharp nose and curvature of the pier, the axe of the scour critical region is almost parallel to the streamwise direction and the maximum shear stresses are near the widest points on the pier surface.
3.4.4 Scour pattern
Figure 3.9. Scour pattern obtained by numerical simulation (upper parts) and corresponding experiments
for piers with different cross-sectional shapes. (Adapted from Khosronejad et al. (2012))
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The shear stress distributions are compared to the scour patterns obtained by laboratory
and numerical experiments conducted by Khosronejad et al. (2012). The test conditions
for their study were similar to this study. The flume was 1.21m wide, the diameter of the
circular cylinder and the width of the square cylinder was 16.51cm and the width of the diamond-shaped pier was 23.35cm. The flow velocity was about 0.2m/s, resulting in
Reynolds numbers in the range of 30,000 to 46,000. The numerical model they developed was based on RANS equation with the k-ω closure coupled with a shear-stress-based sediment transport model and the fluid-structure interaction curvilinear immersed boundary method was used to solve the movable bed.
Since their sediment transport model was based on the bed shear stress, it is reasonable to expect the simulated scour pattern is similar with the shear stress pattern. And comparison between the two (Figure 3.8 and Figure 3.9) does support this initial guess.
The difference between their simulation and the measured scour pattern, however, indicated that the sediment transport model based solely on the traditional bed shear stress was incapable to successfully capture the real scour pattern, especially near the nose region of the circular and square shaped pier. In the nose region for such piers, the calculated shear stresses were relatively small while the scour depths are within 78-98% of the maximum scour depth (Khosronejad et al., 2012). But for the diamond-shaped pier, the simulated pattern corresponded very well with the experiment result. The authors claimed that the major reason was the incapability of the RANS models to resolve the energetic turbulent horseshoe vortex in front of the blunt piers. Another possible cause of such discrepancies is the traditional sediment transport model which ignored the influence of vertical flow. The influence of the vertical flow on scour process is discussed
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earlier in this section and the relatively high downward velocity and larger influence area
in front of the blunt piers (Figure 3.8) may enhance the scour process.
Although the bed shear stress pattern does not match the scour pattern exactly, the maximum shear stress regions indeed correlate to the scour initiation point and the maximum scour locations. For the circular pier, the scour was found to initiate at an angle between 40° to 60° from the streamwise symmetry plane (Khosronejad et al., 2012) and this area is also where the maximum shear stress and maximum scour depth located; for the square and diamond-shaped piers, such areas are located near the two upstream corners (square pier) and two side corners (diamond pier) (Khosronejad et al., 2012). The practical significance of this finding will be discussed latter.
3.5. EFFECT OF ASPECT RATIO
In spite of cross section shape of the pier, the aspect ratio of oblong shaped bridge piers
also have strong effects on altering the flow pattern around piers. In practice, for an
oblong shaped bridge pier, the longer side is often parallel to the major flow direction. In
this section the flow field around oblong shaped piers with different aspect ratios (i.e., 2,
5, 7) is simulated and the attack angles for these simulations are kept as zero.
3.5.1. Vortex structure
Through the comparison of the large vortex distributions (figures are not shown here), it
can be found that the side wall vortexes (Figure 3.6b) for all cases extend to about a
distance of 1B from the nose of the piers; the extending distances of the wake vortexes,
however, are different for piers with different aspect ratio: for the square case (L/B=1),
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the weak vortex extends to a distance of 7B from the downward edge of the pier and this distance is 5B, 3B and 3B for the piers with aspect ratio of 2, 5 and 7, respectively
(Figure 3.10 showed the cases of L/B=2, 7). This may be attributed to the fact that the energy of the separated flow dissipates along the pier and weakens the flow in the wake region.
Figure 3.10. Limited streamline on the plane H/20 over the bed for the oblong piers with L/B=2(a) and
L/B=7(b)
3.5.2 Vertical velocity
Figure 3.11. Vertical velocity distributions along the transverse cut line near the bed in front of the pier.
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The vertical velocity distributions in front of the pier noses and near the bed for different
cases are plotted in Figure 3.11. It can be observed that strong downflow which wraps the
whole nose area exist in all test cases; although there is a trend that the downflow are
stronger for the larger aspect ratio cases, the variation is not significant (less than 10%).
3.5.3 Shear Stress
The shear stress pattern is also studied. The maximum normalized shear stresses for all the four cases are plotted in Figure 3.12, from which it is clear that the variation of the maximum shear stress is relatively small (within 4%, Figure 3.12).
Figure 3.12. Normalized τmax for piers with different aspect ratios
The distributions of the shear stress (Figure 3.13) are similar in terms of magnitude and extension pattern for all the four cases including the square pier case (Figure 3.8b). And oblong piers with round noses are also modeled. The conclusions are similar to the rectangular nose piers. It should be noted that only piers with aspect ratios greater than
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one are simulated since in practice the piers are most installed with the longer side aligned to the main flow.
3.5.4 Scour pattern
From the analysis above, it can be concluded that the aspect ratio of the oblong shaped piers has little effect on the vertical velocity distribution in front of the pier, on the location and magnitude of the maximum shear stress near the bed, and on the overall distribution pattern of the bed shear stress. However, the scour patterns for piers with different aspect ratios are obviously different. Figure 3.14 showed sketches of the scour patterns around piers with different aspect ratios (Briaud et al., 2004). The darker shadow indicates deeper scour.
Figure 3.13. Normalized shear stress near the rectangular piers with different aspect ratios: (a): L/B=2 (b) L/B=5 and (c) L/B=7.
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Figure 3.14. Sketch of the scour pattern around piers with different aspect ratios. (Adapted from Briaud et al. (2004))
It can be concluded that the scour hole around the square one wraps the whole cross section of the pier and extends to a further distance in the downstream direction, compared to other cases; for the high aspect ratio cases, the scour hole is deeper in the front nose and leading corners and the scour in the wake of the piers were negligible
(Briaud et al., 2004). Based on the discussion with the flow pattern and vortex structures discussed previously, a possible mechanism for scour around oblong piers may be the interactions among the down flow in front of the pier, the horseshoe vortex, the side wall vortex and the wake vortex. Around the square pier, the short distance between the upstream edge and the downstream edge make it possible for the merge of the several vortex structures, which enhances the scour process and extends the scour area; for the piers with greater aspect ratio, the horseshoe and side wall vortex dissipate along the pier surface and hence they have little effect on the wake region. On the other side, the upstream flow is harder to “escape” from larger and longer obstructs and thus the energy concentrates on the leading edge of the obstructs and induce deeper scour.
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3.6. EFFECT OF ATTACK ANGLE
For bridge piers located in a river bend or near the river bank or abutment, the flow
direction and the pier direction will not coincide and the angle between the two is called
the attack angle. The attack angle is widely considered to have significant effect on the
flow pattern around piers and thus influence the scour process. What makes the problem
more complicated is that, the attack angle may change progressively due to floods, and
the changes of river bed and river banks over time. In HEC-18, a correction factor for attack angle is proposed to predict local scour around piers (Arneson et al., 2012), and such a factor is related both to the aspect ratio and attack angle, or, the pier projection width (Eq. 3.5); Briaud et al. (2004) studied the effect of attack angle on the maximum shear stress using numerical methods and proposed the correction factor for calculation of the maximum shear stress (Eq. 3.6.).
0.65 L Kα =sinαα + cos (3.5) B
0.57 τ max α kα = =1 + 1.5 (3.6) τ max(0deg) 90
The influence of aspect ratio is not reflected in Eq. 3.6. Instead, it is included in the
global equation for the maximum shear stress in terms of the effective Reynolds number
L (calculated using the projected length B '= sinαα + cos , for details, see (Briaud et al., B
2004). The nose shape effect is not considered in Briaud’s equation. In this section, two series of simulations are conducted to evaluate the effect of attack angle on flow pattern and shear stress around piers. The nose shape of the piers is round instead of rectangular;
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and the aspect ratios of L/B=2 and L/B=4 are simulated respectively; the attach angle is changed from 0 degree to 90 degree with steps of 15 degree.
3.6.1 Flow pattern
Figure 3.15. Limited stream line around round-nosed oblong piers with different attack angle (L/B=4): (a)
α=30° (b) α=60° and (c) α=90°
Selected streamline snapshots near the bed for round-nose piers with aspect ratio of 4 are shown in Figure 3.15. From the figure, it can be observed that, (1) with increasing attack angle, the separation point at upstream moves from the original point, i.e. the round nose, to the center of the pier length; (2) the movement of the separation line results in wider ranges of reverse flow and stronger horseshoe vortex at upstream directing outwards from the pier; and based on the continuity of the flow, there must be stronger downflow in this region; (3) at the downstream side, the wake vortex evolves to two vortexes shed from the two ends of the pier and this accompanies with stronger upward flow and flow towards the pier body.
3.6.2. Shear stress
The normalized shear stress distributions for attack angles of 30°, 60° and 90° are plotted in Figure 3.16. The effect of attack angle on bed shear stress is obvious: (1) the maximum shear stresses increase with the attack angle; (2) the scour critical zone tends to extend to
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larger areas with greater attack angles; (3) at small attack angles, the critical zone near the downstream end of the pier is much larger than the upstream end; and with the increase of the attack angle, this difference decreases.
Figure 3.16. Normalized bed shear stress around round-nosed oblong piers with different attack angle
(L/B=4): (a) α=30° (b) α=60° and (c) α=90°
To evaluate the effect of attack angle quasi-quantitatively, three parameters were defined:
τ max_ α (1) the maximum shear stress ratio rmax = , which indicates the angle effect on τ max_ zero
Acz _α the maximum shear stress (2) the scour critical zone ratio rcz = , which evaluates Acz_ zero
τ ≥ the angle effect on the scour critical area. Aczα and Acz_zero are the total area where 1 τ crit for the cases with attack angle α of and zero, respectively; and (3) the weighted scour
τ ∫ 'dAcz _α r = critical zone ratio cz_ w τ , which reveal the angle effect on the overall ∫ 'dAcz_ zero potential or severity for scour.
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(a)
(b)
Figure 3.17. The maximum shear stress ratio, the scour critical zone area ratio and the weighted scour
critical zone area ratio at different attack angles (round nose). (a) L/B=2 and (b) L/B=4.
rmax , rcz and rcz_w are plotted for conditions with different attack angles and different aspect ratios in Figure 3.17. Several trends can be observed in Figure 3.17: (1) rcz and rcz_w increases with attack angle, indicating that the larger attack angles induce larger and deeper scour holes; (2) Another clear trend is that for piers with larger aspect ratios, rcz and rcz_w are much larger than those for smaller aspect ratio cases. A direct result of this
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trend is that, for larger aspect ratio piers, the scour would be more severe; (3) For piers with aspect ratio of 2, while the maximum shear stress can be amplified up to 2.1-fold by the effect of attack angle, the area of the critical scour zone dose not expand too much
(with a peak rcz value of 1.24); for piers with aspect ratio of 4, however, while the peak value of rmax is 3.6, the rcz value can reach 16, indicating the critical scour zone is greatly enlarged.
Figure 3.18. The maximum shear stress ratio at different attack angles and corresponding fitting curves.
To quantify the effect of attack angle on the maximum shear stress, rmax values for different aspect ratios are plotted with attack angles in Figure 3.18. It can be found that, the rmax value does not increase monotonically and it shows decreasing trend at attack angle of around 75 degree. In fact, as the attack angle changes, the effective width of the pier also increases, which also affect the flow pattern. Therefore, it is reasonable to apply
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the concept of projected pier width to descript the effect of attack angle. As discussed earlier, such a concept is employed to define the attack angle correction factor for scour depth prediction (Eq. 3.5). A similar form of expression is adopted to relate the effect of attack angle on the maximum bed shear stress to both the attack angle and aspect ratio
(Eq. 3.7).
n L rmax =sinαα + cos (3.7) B
The exponent index n is obtained using regression method and the best fit is found to be
0.9 (Figure 3.18). In Figure 3.18, also plotted are the points (blue) reported by Briaud et al. (2004) and their predicting curve (Eq. 3.6). In their simulation, the aspect ratio is 4 and the pier has rectangular shaped nose. The expression of their correction factor (Eq.
3.6) does not include the effect of the aspect ratio, which is revealed in the numerical model (Eq. 3.7).
3.6.3. Scour pattern
The shape of scour hole around a skewed pier with rectangular nose is sketched in Figure
3.19 (from Briaud et al. 2004). It is interesting to find that, with the same numbering of the four corners shown in Figure 3.19, the prediction of the scour shape (Figure 3.15) from the CFD model for the piers with round nose is not consistent with the experimental results for the piers with rectangular nose. While the primary and secondary scour hole around rectangular-nose pier always develops at the corner (1) and (3) respectively, the models presented in this Chapter predicts the primary and secondary critical scour zone for piers with round nose occurs at corner (3) and (1), respectively. The skewed piers
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with rectangular nose are also modeled, and results are consistent with the work by
Briaud et al. (2004). Together with the findings in Section 3.4 (effect of pier shape), it is reasonable to make a hypothesis that such discrepancy between the scour pattern and predicted critical scour zone is caused by the effect of pier nose. But this statement needs further verification through experiments.
(a) (b)
Figure 3.19. Sketch of the scour pattern around piers with attack angle of 15° (a) and 30° (b). (Adapted from Briaud et al. (2004))
From all the analysis in this section, it is concluded that the flow around a pier can be affected by various factors including as the shape, aspect ratio and skew angles of the pier.
3.7. IMPLICATION TO SCOUR MECHANISM AND PRACTICAL SIGNIFICANCE
In previous analysis, attempts are made to relate the flow patterns to the scour patterns for different test cases. From the comparisons, an important conclusion is that the scour pattern is not only dependent on the bed shear stress; downflow, and the interactions of the primary vortexes may also play important roles in the process of scouring. The popular sediment transport models (for example, Engelund and Fredsøe, 1976; van Rijn,
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1984; Meyer-Peter and Muller, 1984), which are based on the critical shear stress theory
will have problem when used to model the scour process around bridge piers. To
overcome such limitations, one solution is to developed new sediment transport models
through experiments in which the turbulent flow can be well controlled and the
interaction between sediments and coherent vortex structures can be characterized
effectively; an alternative path is developing numerical models which can not only
capture the energetic turbulent structures but also couple the particle movements with the
resolved flow. The former requires elaborate sensing and controlling system; super
computational resources, efficient algorithm and physics-based particle-fluid coupling models are vital for the success of the latter approach. Recently, Escauriaza and
Sotiropoulus (2011a) reported their newly developed Lagrangian model to study the sediment-turbulent interaction and such an approach also inspired them to study the initial stage of bridge scour in turbulent flow (2011b).
The findings in this research also have practical significance such as assistance in bridge scour risk analysis, countermeasures design and scour monitoring planning and etc. In spite of the maximum scour depth, the prediction of the time dependent scour depth or the scour depth versus time curve is also important for bridge scour risk analysis. In the scour rate in cohesive soils (SRICOS) Method (Briaud et al., 2004), two fundamental parameters define such a curve: one is the initial scour rate and the other is the final maximum scour depth. For the estimation of the initial scour rate, the maximum shear stress on the initial flat bed is first obtained and this value is then used to read the initial scour rate on the erosion function obtained in the erosion function apparatus (EFA) test
(Briaud et al., 2004). In Briaud et al. (2004), an equation is proposed to estimate the
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maximum shear stress for complex piers by modifying the τmax for the circular pier, which
is obtained using an empirical equation. To improve the estimating accuracy of the initial
scour rate, τmax can be directly obtained using the 3D flow model used in this research.
For the riprap design, HEC-23 (Lagasse et al., 2012) recommends the Eq. 3.8 for the
sizing of the rock riprap and underscored the selection for the value of Vdes (design
velocity for local conditions at the pier), which should be the velocity immediate vicinity
of the bridge pier.
2 0.692(Vdes ) d50 _ riprap = (3.8) (Sgg −12)
where d50-riprap is the median rock diameter, Sg is the specific gravity of riprap, and g the
acceleration due to gravity.
When the average velocity or the velocity distribution from 1-D and 2-D computational
software (such as HEC-RAS) is used as Vdes, correction factors such as the shape factor and the location factors should be used. And all the rude factors are obtained from limited laboratory experiments. Since the three-dimensional flow model in this research can estimate the flow field with high accuracy, the using of the velocity calculated with this model in Eq. 3.8 is expected to improve the confidence for sizing the riprap for scour countermeasure.
For the measurement and monitoring of the bridge scour, fixed and buried systems are
often used for long term monitoring purpose. Such systems include sounding rod,
magnetic sliding collar, Time Domain Reflectometers (TDR) rod or strips and even
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buried float transmitters and fixed sonar devices, etc. ( Lagasse et al., 2012). An important issue is where to install such systems. Since the cost of these systems are typically high, one should determine the location in prior of installation to make it most effective. Since the maximum shear stress location often indicates the maximum depth location, the findings about the maximum shear stress for piers with different shapes, aspect ratios and skew angles in this study can serve as a guide for the installation of the fixed and buried scour monitoring system.
3.8. RECOMMENDATIONS TOWARD MODELING OF THE SCOUR PROCESS
In the previous Sections in this Chapter, the flow structures around piers are modeled and analyzed. In this Section, recommendations toward modeling of the scour process are made.
3.8.1. The framework
The flow chart of this framework is illustrated in Figure 3.20. The simulation starts with the initial river bed. With the CFD flow model, the flow field and bed shear stress distribution around bridge piers can be obtained. The sediment transport models (bedload and suspended load) are coupled to the flow model. And the changing of the sediment concentration is then coupled to a bed morphodynamic model, from which the change of the bed elevation can be calculated. The evolution of the scour hole will also affect the flow field. To update the scoured bedform, the Arbitrary Lagrangian Eulerian (ALE) method is utilized to update the moving mesh of the simulation domains. This process continues until equilibrium reaches.
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Figure 3.20. The flow chart for modeling of the scour process
3.8.1.1. The bed morphodynamic model
The direct consequence of bridge scour is the change of the bedform. The change of bed elevation is studied from 1920s since Exner (1925) proposed the relationship between the rate of change of the bed elevation and the spatial variation of the local sediment flux based on the sediment mass balance. In addition, it becomes standard to include the temporal changes in the local sediment concentration to represent the unsteadiness of sediment transport (Paola and Voller, 2005). In practice, various forms of sediment mass balance equations has been employed as the morphodynamic model and to unify all the expressions, Paola and Voller (2005) derived a generalized Exner equation for sediment
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mass balance. Therefore, the standard expression of the Exner equation derived by Paola
and Voller are often referred as the Exner-Paola equation (Eq. 3.9).
∂zb −∂1 γ = ∇⋅q + (3.9) ∂∂ tt(1− λp )
In Eq. 3.9, zb is the bed elevation; λp is the porosity of the bed material and its value is
assumed as constant and equals to 0.35-0.4 for fine sands; q is the sediment flux vector which is the volume of sediment transported per unit length in unit time (and the dimension of the sediment flux in any direction is [m2/s]) ; the sediment flux is the due to
the combination of bedload qb and the suspended load qs; and cb is the areal concentration
with dimension of [m].
The Exner model is the basis for almost all the existing numerical scour models in the
literatures. Based on different assumptions, the Exner equation has different formulations:
(i) Assuming the local sediment concentration is steady and only the bedload
∂γ contributes to the scour, the term in Eq. 3.9 is neglected (Eq. 3.9-1) and such a ∂t
formulation was applied in many studies to simplify the calculations (such as in Roulund
et al. 2005, Apsley and Stansby 2008, Khosronejad et al. 2012);
∂z −1 b = ∇⋅q (3.9-1) ∂ b t (1− λp )
(ii) Assuming the local sediment concentration is unsteady and only the bedload is
considered, the Exner equation is in the same form of Eq. 3.9 but with the q replaced with
qb (Eq. 3.9-2). This formulation is employed in Escauriaza and Sotiropoulos (2011b).
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∂zb −∂1 γ = ∇⋅qb + (3.9-2) ∂∂ tt(1− λp )
(iii) Assuming the local sediment concentration is steady and the suspended load
∂γ can be expressed using explicit empirical descriptions, the term can be replaced with ∂t the entrainment rate Es minus the deposition rate Db (or) and therefore the bed elevation can be expressed as Eq.5-3.
∂z −1 b =( ∇⋅q +ED − ) (3.9-3) ∂ bss t (1− λp )
The deposition rate at the bed is Ds= wc sb,where the ws is the following velocity of sediment particle in the still fluid and cb is the sediment concentration at the bed; and the
entrainment rate at the bed is Es= wc sa ,where ca is a reference concentration (also called as the dimensionless entrainment rate) with empirical models (for example, Smith and
Mclean 1997, van Rijn 1984b, Garcia and Parker 1991, and these models are summarized in Liu and Garcia 2008). The Exner equation in the form of Eq. 3.9-3 is selected to simulate the bridge scour in Liu and Garcia 2008 and Zhao et al. 2010.
3.8.1.2. The sediment transport models
From the bed morphodynamic models, it is clear that the accuracy of the models depends on the description of the sediment flux vector and the rate of sediment areal concentration on the bed. Conventionally, the sediment flux and concentrations can be calculated using sediment transport models and various models are available for the transport of the bedload and suspended load. The commonly used models are briefly presented in this section and the key parameters in such models are discussed to illustrate their importance.
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(1) Suspended load
The suspended load is the sediment carried by the flow with very small settle velocity and therefore is assumed to travel above the bed load layer. The suspended load can be evaluated using the sediment volume concentration (c), which can be expressed by the
convection-diffusion equation (Eq. 3.10).
∂c g +∇⋅ − =∇⋅ν ∇ u wcsc( c) (3.10) ∂t g
In Eq. 3.10, u is the flow velocity vector which can be determined by the turbulence
model described in Section 3.2 and νc is the diffusion coefficient and it can be related to
ν t the flow eddy viscosity as ν = (Abbasnia and Ghiassi, 2010). Sc is the turbulent c Sc
1 Schmidt number and can be calculated following van Rijn (1984b): S = , c 2 w 12+ s u f
where uf is the shear velocity. The determination of uf will be discussed in the following
context. The introduction of Sc includes the effect of the turbulence on reducing the setting velocity of the sediments (Abbasnia and Ghiassi, 2010). However, since the value of Sc tends to be in the range of 0.5-1.0, it is taken as a constant 1 in some bridge scour models (for example, in Liu and Garcia 2008 and Zhao et al. 2010).
(2) Bed load
Different from the suspended load, the bed load are those particles which are transported
along the bed. The bed load are commonly described using empirical or semi-empirical
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equations (for summary of various bed load transport equations, the readers are referred
to Apsley and Stansby 2008, Ouriemi et al. 2009). Most of them are developed for river
bed erosion research and the bed load transport of sediment is quantified by the so called
bed-load flux, often determined by the local bed shear stress and sediment characteristics.
The widely used bed-load transport equations includes (1) Meyer-Peter & Muller equations (1948); (2) Engelund & Fredsøe equations (1976); and (3) van Rijn equations
(1984a, 1987 and 1993) These traditional bed load transport equations are typically based on laminate flow assumptions (using the concept of critical shear stress or critical flow velocity) and uses equilibrium assumptions for the sediment transport. A general expression for the bed-load transport models in the dimensionless form can be written as
(Raudkivi 1990, Apsley and Stansby 2008):
* ** qb = fd(τ , ) (3.11)
In Eq. 3.11, q* is the dimensionless bed-load flux (Eq. 3.11-a); τ* is the dimensionless shear stress or Shields stress (Eq. 3.11-b), which is also often denoted by θ elsewhere in the literature; d* is the dimensionless particle diameter (Eq. 3.11-c).
* qb qb = (3.11-a) (s−1) gd 3
τ τ* = b (3.11-b) ρ (s−1) gd
13 (sg−1) * = dd2 (3.11-c) ν t
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In Eq. 3.11-a,b,c, s and d is the specific density and the diameter of the particle, respectively. The τb in Eq. 3.11-b) is the bed shear stress defined as Eq. 3.12, where uf is the shear velocity.
2 τubf= ρ (3.12)
Most of the functions related the shear stress and particle size to the bed load flux in Eq.
3.11 are based on the excess shear stress hypothesis. And the bed load transport formulas
* often include a τcrit term, which represents the critical shear stress at which the incipient motion of sediment particles occurs. It should be noted, however, that there are other hypotheses to predict the incipient motions other than the excess shear stress approach.
For example, the critical velocity method determines the incipient motion of sediment particles by the excess velocity (such as by Yang, 1973). Comparison among several shear-stress based methods and the velocity based methods were made by Marsh et al.
(2004) and it was found that the performances of the shear stress methods were superior to that of the velocity method. Hence, we adopt the shear stress methods in our framework and here we selected the aforementioned three formulas.
* **23 qb =8(ττ − crit ) (3.13)
2.1 0.053 ττ**− q* = 8 crit b * 0.3 * (3.14) d τcrit
− 4 14 π 16πµ * = + d qUbb0.5 1 (3.15) * 13 ττ**− 61d( sg− ) ν t crit
Eq. 3.13 is the Meyer-Peter & Muller equations (1948) (used, for example, by Onda et al.
* 2008, Guven and Gunal 2010, etc.), in which τcrit is assumed to be a constant (0.047); Eq.
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3.14 is the van Rijn equations (1984a) (used for example by Liang et al. 2005, Zhao and
Cheng 2008, Zeng et al. 2010, Zhang et al. 2011); and Eq. 3.15 is the Engelund &
Fredsøe equations (1976) (used, for example, by Roulund et al. 2005, Nakamura et al.
2005, Liu and Garcia 2008, and Zhao et al. 2010, Nakamura et al. 2011), in which μd is
the dynamic friction coefficient and Ub is the mean transport velocity of a particle
moving as bedload and is suggested as a fraction of the shear velocity
=⋅−** − ( Uub f a(1 0.7 ττcrit ) , where a is a constant).
3.8.2. An in-depth view on the bed load formulas
As for the sediment transport models, although a variety of models are available to
simulate erosion and scour, the reasons on the choice of a certain bedload formula and the
corresponding parameters are seldom explained. In fact, such formulas are mostly developed based on the laboratory experiments or semi-analytical deductions for the bed
load transport in undisturbed flow on the flat bed. Here, “undisturbed” means the flow are
not disturbed by embedded obstacles. Strictly, such formulas cannot be used directly in
the case of bridge scour, where the flow is highly turbulent and disturbed and the scoured
bed will no longer be flat. Therefore, modifications have to be made to employ the
traditional bed load formulas to simulate the bridge local scour. In addition, no
comparisons on the performance of the formulas are made and it becomes difficult to
evaluate the capability of each formula. Once the disturbed flow is resolved or modeled,
the sediment transport model becomes the only key to predict the evolution of the scour.
Therefore, a comparison of the performance of different sediment transport models is valuable and beneficial for future researches. In addition, in most numerical models, the
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scour hole is under predicted to certain extents (for example, in Olsen and Melaaen
(1993), Roulund et al. (2005) and Zhao et al. (2010). Therefore, there is a need to improve the scour model, especially the sediment transport model and to modify it to be suitable for bridge scour simulations.
When only the bedload is considered (clear water condition), the combination of a certain bed load formula (Eq. 3.13, 3.14, 3.15) and the Exner equation (Eq. 3.9-1, 3.9-2) can give the bedform changing rate. It is clear that the dominant parameters of the bed load flux are the shear stress and the critical shear stress. Although these formulas are widely employed to simulate erosion and scour as we summarized above, the reasons on the choice of a certain bedload formula and its related parameters are seldom explained. In fact, such formulas are mostly developed based on the laboratory experiments or semi- analytical deductions for the bed load transport in undisturbed flow on the flat bed. Here,
“undisturbed” means the flow are not disturbed by embedded obstacles. Strictly, such formulas cannot be used directly in the case of bridge scour, where the flow is highly turbulent and disturbed and the scoured bed will no longer be flat. Therefore, modifications have to be made to employ the traditional bed load formulas to simulate the bridge local scour. In addition, no comparisons on the performance of the formulas are made and it becomes difficult to evaluate the capability of each formula. In this section, the parameters in the bed load transport formulas are discussed in depth to illustrate the importance of the choice of such parameters.
τ* 3.8.2.1. Critical shear stress crit
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Through experimental data, Shields (1936) found that the non-dimensional critical shear stress can be related to the Reynolds number (Red*) of the particles through a curve which is refereed as Shields curve later. The Reynolds number of the particle is given by,
* udf Red = (3.16) ν t
A drawback of the Shields curve is the critical shear stress can only be obtained by trial
* * and error methods iteratively because τcrit and Red both contain the shear velocity term and thus are interchangeable (Eq. 3.11-b, 12 and Eq. 3.16). Various empirical formulae have been proposed to describe the Shields curve explicitly and summaries of such formulae can be found in Yalin (1972), Zankie (1996) and Soulsby (1997). A widely used prediction formulae is provided by Soulsby (1997) (Eq. 3.17).
**0.30 τ crit = +0.055 1 −− exp( 0.020d ) (3.17) 1+ 1.2d *
A recent comparison of different formulae and functions proposed for Shields type diagram suggested the use of the single curve proposed by Paphitis (2001) (Eq. 3.18) due to its high correlation coefficients and low errors.
* 0.273 * *4 τ crit = +0.046 1 − 0.576exp( − 0.020d ) , ( 0.01<< Red 10 ) (3.18) 1+ 1.2d *
Comparing Eq. 3.17 and Eq. 3.18, it is obvious that they have the same mathematical form except that certain coefficient constants are different.
3.8.2.2. Bed shear stress τb
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From the definition of the bed shear stress (Eq. 3.12), the key factor affect it is the shear
velocity on bed. In experiments, the shear velocity can be related with mean velocity or
near-bed velocity based on different assumptions. For example, it can be related with the
mean velocity with a particle dependent Chezy-coefficient (as in van Rijn (1984a); it can
also be related with the gradient of velocity near the bed; a more widely applied method
is based on the logarithmic law of the velocity profile. Since the last approach is more
suitable for numerical simulations in RANS scheme (the wall functions for the
boundaries in such models are also described by the logarithmic law), it is adopted in our
framework.
Different formation of the logarithmic law of the velocity profile exists and it is related to
the wall functions used for the bed boundary in the RANS scheme. With different wall
functions, the formation of the shear velocity may vary; the readers are referred to
Roulund et al. (2005), Zhao et al. (2010) and Khosronejad et al. (2011) for examples.
The wall function we used in our simulation is modified the formulation of Kuzmin and
Mierka (2006) for k-ω turbulence model. In this formulation, the shear velocity can be
related to the tangential velocity with Eq. 3.19.
y** yy≤ u + ++ t = 1 * (3.19) u f log y++>β0 yy ++ κ
In Eq. 3.19, ut is the tangential velocity; κ is the Karaman constant with the value of 0.41;
uyf y+ is the local Reynolds number defined as y+ = , where y is the distance from the ν t
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* wall boundary; y+ is a constant (11.06 in this framework); β0 is a constant with value of
5.2 for smooth walls.
3.8.3. Modification on the critical shear stress
3.8.3.1. Slope correction
As mentioned before, the original Shields curve is based on the results of tests on flat bed.
When there is slope on the bed, the effective weight of the particle will decrease and the fluid forces acted on the particle will also change. For a scoured bed, the slope can be big and modifications on the critical shear stress should be made. The modified critical shear
* stress can be expressed as the original one (τ crit ) multiplied with a reduction factor rs
* (Bihs and Olsen, 2011) (Eq. 3.20), where the τ crit can be determined using Eq. 3.17 or Eq.
3.18.
** ττcrit, s=r s ⋅ crit (3.20)
Different formulation of r was proposed in recent years and examples are the work of
Lane (1955), Ikeda (1982), Kovacs and Parker (1994) (or Seminara et al. (2002)) and
Dey (2003). Bihs and Olsen (2011) compared the performance of the different reduction factors proposed by these authors and concluded that the Kovacs and Parker’s method and the Dey’s method was most suitable for the prediction of abutment scour. Both of these two formulae take the transversal and longitudinal sloping into account. In addition, the lift force is also included in their formulae. Since the Dey’s formula is in an explicit analytical expression and the Kovacs and Parker’s expression is in a quadratic equation form, the Dey’s formula (Eq. 3.21) is selected in our framework.
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−+sinθη tan222 ϕ cos θ − sin α + ( ) 2 1 222 rs = sinθη+− tan ϕ cos θ sin α (3.21) (1−ηϕ tan) tan ϕ( ) 0.5 +−η22222222 ϕ ⋅ θϕ − αϕ − θ − α (1 tan) ( cos tan sin tan sin sin )
In Eq. 3.21, α is the transversal angle, θ is the longitudinal angle and φ is the angle of repose of the sediment. η is the lift/drag force ratio, which was set as a constant value
0.85 in Bihs and Olsen (2011), more information of this ratio will be discussed later.
3.8.3.2. The influence of turbulence and lift force
As mentioned earlier, the Shields curve cannot be directly applied to the context of bridge scour, where the flow is highly disturbed. Experimental researches indicate that the horseshoe vertex (or external turbulent) in front of the piers would enhance the scour and the scour can be initiated before the bed shear stress exceeds the critical shear stress determined by the Shields curve (Sumer, 2003). The influence of external turbulence on bed load sediment transport was studied by Sumer et al. 2003 and Okayasu et al. 2010. It was found that the increase in the turbulence level can induce 6 fold of increase in sediment transport (Sumer et al. 2003). In the existing numerical scour simulations, however, the influence of the turbulence on the critical shear stress is not incorporated. In addition, the lift force on the sediment particles are neglected in Shields curve, but the lift force cannot be neglected especially at high fluctuating flows. The effective weights of sediment particles will be deduced due to the lift force and thus make the particles more prone to be scoured.
Similar with the slope correction, the influence of turbulence and lift force can be taken into account by introducing another modification factors, rt and rl. An analytical solution
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of such a factor was obtained by Zanke (2003). The analytical solution of the critical
shear stress for turbulent flow can be rewritten as Eq. 3.22.
1 ττ**= crit, t 2 crit (3.22) ucb′, F 1++ 1L tanϕ uFbD
In Eq. 3.22, ub and ucb′, is the mean bed velocity and the fluctuation part, the ratio of the
two can be termed as the turbulence intensity I and thus rt is an function of I (Eq. 3.23).
FL and FD is the lift force and the drag force on the particle, respectively; and the ratio between the two is denoted as η and thus rl is a function of η (Eq. 3.24).
1 = rt 2 (3.23) (1+ I )
1 r = (3.24) l (1+ηϕ tan )
To incorporate all the influences from sloping bed, turbulence and lift force, the overall
modification factor (R) to the critical shear stress is the product of the three correction
factors (Eq. 3.25).
** * ττcritm, =R ⋅ crit ≡( rrr s ⋅⋅ t l) ⋅ τ crit (3.25)
It should be noted that if the lift/drag ratio has been included in the sloping bed correction
(for example, Eq. 3.21), the lift force correction factor in Eq. 3.25 should take the value
of unit 1. Eq. 3.21, 3.23 and Eq. 3.24 indicates all the three factors are less than one,
therefore, it can be concluded that the overall effect of the sloping bed, turbulence and lift
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force will reduce the critical shear stress. And this is consistent with experiments observations (Sumer 2003).
3.8.4. Alternative modification method for the bed load transport equations
Instead of modifying the critical shear stress as discussed in Section 3.8.3 in this section, the formulation of the shear stress can be modified to incorporate the influence of turbulence. Abbasnia and Ghiassi (2011) proposed a modification on the bed shear stress formulation for pier scour computation by including a centripetal force due to the effect
* of vorticity. In this paper, we define a non-dimensional stress (τ c ) due to the centripetal force (Eq. 3.26) and the modified bed shear stress (Eq. 3.27) is proposed based on the assumption of Abbasnia and Ghiassi (2011).
1 ρωu τωsc su τ * =≡≡cc3 (3.26) c ρρ(sg− 1) ( sg −− 1) 3( sg 1)
* *2 2 *2 τmc= τ + ϑτ (3.27)
In Eq. 3.26, τc is the vorticity induced shear stress on the particles; ρs is the particle density; and ωc is the vorticity at the position of the particles. In Eq. 3.27, ϑ is a reduction coefficient and the value ranging from 0.4 to 0.7 is recommended for cases in clear water and for rounded sediment particles (Abbasnia and Ghiassi (2011).
It is worth noting that the modifications to the bed load transport equations proposed in
Section 3.8.3 and Section 3.8.4 are based on different assumptions to incorporate the
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influence of turbulence, and it is not recommended to apply both the modifications to the
original bed load transport models at the same time.
3.9. SUMMARY AND CONCLUSIONS
Three dimensional CFD simulations are carried out to study the effect of pier configurations on the flow pattern and bed shear stresses. Configurations of piers include different cross-sectional shapes, namely circular, square, diamond and lenticular; different aspect ratios; and different angles of attack. The vortex structures, vertical velocities and bed shear stress around the piers with each configuration are analyzed and compared.
The main findings include:
• Cross-sectional shapes can dramatically affect the flow pattern. For piers with
blunt noses, strong downward flows exist in front of the piers; for piers with sharp
noses, the flow pattern is dominated by the separated shear layers;
• At most of the time, the location of maximum shear stress corresponds to
maximum scour depth; but the differences between the scour critical zone
(evaluated by shear stress) and the scour pattern indicate that other factors instead
of shear stress also play an important role in the process of scour. Through
analysis, such factors include the downflow and the interactions between different
vortex structures;
• The aspect ratios for oblong piers has little effect on the maximum shear stress
and the overall distribution pattern for the bed shear stress; it does affect the
interactions between the horseshoe vortex, the side wall vortex and the wake
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vortex, which causes the different scour patterns for piers with different aspect
ratios;
• Attack angle has severe influence on the flow patterns around piers; with higher
aspect ratios, the degree of such influence increases. An equation in the form of
an exponential of the effective pier width is also proposed to evaluate the
combined effect of the aspect ratio and attack angle.
• From these findings, implications for the scour mechanism and future
modifications on the existing sediment transport models for scour modeling
purpose are discussed; also underscored are the possible applications of the CFD
modeling approach on practical engineering areas such as initial scour rate
estimation, design guidance for bridge scour countermeasure and monitoring
plans.
In this Chapter, also presented is a framework to simulate bridge scour using CFD
technique and sediment transport models. Efforts are made to review the existing
sediment transport models with in-depth discussions. It is worth noting that such
sediment transport models are mostly developed based on the assumption of undisturbed
flow in flat bed. Strictly speaking, they cannot be directly employed in the case of bridge
scour, where the flow field is highly disturbed and turbulent flow dominates. Therefore,
modifications should be made to incorporate the influence of turbulence and sloping bed.
A new formation of the critical shear stress in the traditional methods was proposed by
including modification factors such as sloping bed factor, turbulence factor and lift force
factor. The overall effect of the factors was found to reduce the critical shear stress and this may lead to earlier incipient of scour and deeper final scour depth than traditional
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models. In fact, as mentioned in the previous context, the scour hole was under-predicted to certain extent in most existing numerical models (for example, in Olsen and Melaaen
(1993), Roulund et al. (2005) and Zhao et al. (2010). Therefore, the newly proposed sediment transport model is expected to improve the overall prediction capability of the numerical scour models.
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CHAPTER 4
FROM BIO-INSPIRATION TO BIO-MIMICKING: A MULTIDISCIPLINARY
REVIEW ON HAIR FLOW SENSOR
4.1. INTRODUCTION
In order to relate the initiation of bed sediment to the turbulence from experiments either
in the laboratory setup or the field setup, the first task is to characterize the turbulence.
This objective requires that the flow sensors possess capabilities such as multi-
dimensional mapping, low-detection threshold, short response time, least intrusion to the
flow field of interests, and low costs and high durability (Chen et al 2003). Traditional
flow sensing methods such as Hot-Wire Anemometry (HWA), turbine flow meters, acoustic Doppler-shift velocimetry and Particle Image Velocimetry (PIV) cannot fulfill these requirements due to their large size, low sensitivity, complex set-up, etc. (Fan et al
2002).
Nature has always been a source of inspiration and serves as a guide for technical
developments (Fratzl and Barth 2009, Stroble et al 2009). Creatures live in different medium, i.e., fishes in the water, flies in the air, and earthworms in the sand or mud.
Some of these mediums are changing rapidly and therefore, creatures in them are equipped with flow sensitive sensors in order to survive in these changing complex environments. It is inspiring to learn from nature and develop artificial counterparts that emulate such high-performance biological flow sensors.
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The researches on natural hair flow sensors have just begun and only a few attempts have been made to create biomimetic sensors. This Chapter intends to provide a comprehensive review on bio-inspired hair flow sensors, which includes the basic sensing mechanisms in biological hair flow sensors and what have been achieved on biomimetic devices to date. The bio-inspirations at different levels, namely hair morphology, sensing mechanism, information processing etc. are highlighted to emphasize that only through a multi-level mimicking strategy can high-performance be achieved in artificial hair flow sensors.
4.2. BIO-INSPIRATION: LATERAL LINE SYSTEM OF AQUATICS
The lateral line (Figure 4.1), which is a spatially distributed system of directional flow sensors and can be found in all cartilaginous and bony fishes and aquatic amphibians, has been studied extensively in the past few decades (Dijkgraaf 1963, Coombs 2001).
Relying on the lateral line system, at least mainly relying on it, fishes “feel” low frequency (<200Hz) water motions created either by steady flow or turbulent flow. This information is then processed by its central nervous system to guide a number of different behavioral abilities such as orienting, schooling and preying (Coombs 2001).
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Figure 4.1. The lateral line system of fishes. (a) Neuromasts distribution in Lake Michigan mottled sculpin,
black dots in the red shaded canal area represent the CNs and dots in other areas are SNs (modified from
Coombs (2001);. (b) The neuromasts canal diagram4, typically between an adjacent pore pair, there is one
CN (CILIA, 2008); (c) A SN with Cupula is examined with optic approaches and the kinocilia are visible
(modified from McHenry and van Netten, 2007 and the kinocilia are highlighted in yellow for better
illustration); (d) A neuromast of zebra fish (modified from Roberts et al 2009). This neuromast consist of seven hair cells and the white arrows indicate that the staircase directions for two groups of hair bundles are
nearly opposite.
4.2.1. Number and distribution of Canal Neuromasts (CNs) and Superficial
Neuromasts (SNs)
Hair cell numbers in neuromasts vary greatly, but typically a SN contains tens of hair cells and a CN contains hundreds to thousands of hair cells (van Netten 2006). The numbers and distributions of SNs and CNs are believed to represent an adaption to a particular hydrodynamic environment. Still water habitats are often related to the
4fish: lateral line system of a fish. [Art]. Encyclopædia Britannica Online. Retrieved 16 December 2011, from http://www.britannica.com/EBchecked/media/3409/Lateral-line-system-of-a-fish
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supernumerary SNs, widen canals and reduced canal lengths while turbulent aquatic
environments are often associated with fishes with less SNs and narrower canals
(Schellart et al 1992, Bleckmann 1994, Engelmann et al 2002). It is thought that adult
fish, which have complete systems of lateral line canals, are capable of localizing the
prey stimuli from spatial variation in the pressure gradients along the trunk(Coombs and
Conley 1997a,b, Curcic-Blake and van Netten 2006); On the other hand, larvae, which
are much smaller than the scale of prey stimuli (Higham et al 2006) and on which only
SNs exist, can only detect a wide range of flow velocities and the high variability in the
frequency responses of their SNs may hinder an ability to sense spatial cues (van Trump
and McHenry 2008).
To engineers, these findings of course can shed some light on the design of flow sensors
for different applications. For instance, for steady flow applications we can learn more
from the SNs and for the turbulent sensing, CNs-type design may be more suitable.
However, recent detailed studies (Beckmann et al 2010, Klein et al 2011) found that the
number of SNs did not clearly predict the hydrodynamic environment. Therefore, to
further uncover the sensing mechanism of the lateral line system, more information about
the detailed anatomy of the peripheral lateral line and the physiology of SNs and CNs,
their cooperation and the processing of stimuli in the central nerve system are required
(CILIA report 2008).
4.2.2. Directional sensitivity
The directional sensitivity of the lateral line enables fishes to locate stimulus sources. The
directional sensitivity of a single neuromast is due to the staircase structure of the hair
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cell, in which a bundle of relatively short stereocilia with increasing heights followed by a longer kinocilium (Figure 4.1(d)). The direction of the bundle’s staircase is along the long axis of the canal for CNs and parallel to the long cross-sectional axis of cupula (van
Netten 2006), and SNs are oriented in line which is either parallel or perpendicular to the nearby canal axis (Kroese and Schellart 1992). Depolarizing of the cell occurs when the stereociliary bundle bends towards the kinocilium, simultaneously with an increasing in the firing rate of afferent fibers, and vice versa (Coombs, 2001). Along the intermediate directions, displacement of the stereociliary bundle results in responses that are an approximate cosine function of the input direction (Flock 1965). Since hair cells on each neuromast are oriented in two opposing directions (Coombs 2001), the overall directional sensitivity of a neuromast also follows a cosine function. This directional feature of the neuromasts, together with the distribution of neuromasts in different part of the fish body, may form the mechanism of how fish determine the water-flow direction and even the regional hydrodynamic variations from different stimuli (Montgomery et al 2000).
Furthermore, a recent study reveals that the existence of flush ridges around the stereotyped array of SNs in the cephalic lateral line of the surface feeding killifish will change the hydrodynamic environment of the SNs and as a result modify the directional receptive range of this species (Schwarz et al 2011). Such information all has implications for the development of artificial flow sensors.
4.2.3. Flow sensing mechanism: experimental discoveries and biomechanical sensing model
Due to differences in the morphology and hydrodynamic environment, CNs and SNs also differ from each other in terms of sensing mechanisms and functions.
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4.2.3.1. Experimental findings
The firing rates of the afferent fibers are controlled by the displacements of the neuromasts (Flock 1965). When the hair bundles were displaced towards the kinocilium, the afferent firing rates increase and vice versa. Afferents can increase their firing rate in response to hydrodynamic deflections of a single neuromast (Catton et al 2007). The existence of the cupula couples the motion of the surrounding water to the underlying cilia through viscous forces (Coombs 2001). Kroese and van Netten (1987) reported that the neural response is proportional to the displacement of the cupula, and in the meanwhile, the displacement of the cupula is largely proportional to the velocity of the flowing water. Montgomery et al (2000) also established a linear relationship between the responses of the SNs of the eel and the different stimuli with variable flow velocities.
These findings indicate that the neurophysiological response of a neuromast depends on the degree to which cupula mechanics permit the deflection of the kinocilia in response to the water flow (van Trump and McHenry 2008).
Due to the difference in the hydrodynamic environment where CNs and SNs are exposed,
CNs act as a detector of water acceleration while SNs function as a detector of water velocity. This has been proved by the measurements of the motions of the cupula (van
Netten and Kroese 1987), the canal fluid (Denton and Gray 1983) and the response properties of afferent fibers innervate CNs and SNs (Kroese and Schellart 1992, Voigt et al 2000). Biologists have developed theoretical models to unveil the mechanisms of the sensing abilities of the neuromasts and to study their underlying interactions with fluids
(van Netten 2006 (CNs modeling); McHenry et al 2008 (SNs)). All of these theoretical analyses, which will be described in the next context, help to understand the basic sensing
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mechanism and can be referred to in the design of the artificial counterpart of the lateral
line system.
4.2.3.2. Biomechanical Model for CNs
The frequency response of the cupula of CNs of a ruff measured at the top and that
measured at the base was reported identical to each other, which implicates that the
cupula is actually sliding over the sensory epithelium during motion (van Netten and
Kroese 1987). Using laser interferometric techniques, the cupula and canal fluid
dynamics have been determined with nanometer accuracy (reviewed by van Netten 2006).
The response of a CN to the fluid flow was found to be dependent upon the frequency-
dependent flow characteristics and the size and the stiffness of the cupula. From this
result, biologists models the CNs as a rigid hemisphere sliding over a frictionless plate, which is coupled with a linear spring whose stiffness was provided by the underlying hair bundles (Figure 4.2a(i), van Netten and Kroese 1987, van Netten, 1991, van Netten 2006).
In van Netten’s model, the free stream in the canal is modeled as a uniform freestream since it is not greatly influenced by the boundary layer dynamics for the frequency band to which the CNs are sensitive (>20Hz) (van Netten 2006). Furthermore, the uniform stream flow speed in the canal is proportional to the pressure difference between adjacent pores (Denton and Gray 1983, van Netten 2006).
Refer to Figure 4.2a(ii), use the hemisphere as the subject, the governing equation for the dynamics of the CNs reads:
FmKub+=+ F FF (4.1)
MYt()+ KYt () = DYt [ () −+ Wt ()] MWt () (4.2)
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Figure 4.2. Schematic illustrations of CNs and SNs and their responses to hydrodynamic stimulus. a(i) is a
CN between two adjacent pores; and a(ii) illustrates the modeling of the CN responding to a vibration
sphere induced canal flow. The CN can be modeled as a sliding hemisphere, whose deflection (Y) is
induced by the uniform canal flow (Uc).The stimulus is a vibrating sphere (with displacement X and
frequency f), the resulting acceleration along the canal is a. b(i) shows two SNs exposing to the boundary layer near the fish skin. The color gradient of the flow (blue) illustrates the velocity profile in the boundary
layer; b(ii) illustrates the response of a single SN to a near vibrating sphere. V0 is the vibrating velocity of
the sphere, Uh is the local velocity in the boundary layer and ν is the deflection of the cupula at the height
of the longest stereocilia (McHenry and van Netten 2007); b(iii) illustrates a model for a SN responding to
a freestream (U0). in which, on the left hand side are the structural forces and on the right hand side are the
hydrodynamic forces. In detail, Fm = MY() t is the structural inertial force of the hemisphere where M and Y is the mass and the displacement of the CN, respectively;
Fk = KY() t is the structural stiffness resistance of the hemisphere due to the elastic
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coupling of the hair bundles to the epithelium, with K, the sliding stiffness which is
proportional to the number of hair cells; F= DY[ () t − W ()] t is the hydrodynamic drag u force acting on the hemisphere, here D is the drag coefficient, W is the displacement of the water; and F= MW () t is the buoyance force acting on the hemisphere due to the b pressure differences around the structure.
Due to the linearity of the governing equation, the frequency-dependent cupula sensitivity
Sf() ( YU0 ), which is defined as the ration of displacement amplitude (Y0(f), which is a
function of the stimuli frequency f) to the amplitude of excitatory fluid velocity (U0) can
be obtained by solving the governing equation. The solution is given by (van Netten
2006):
1 11 1++ 2(1ii )Re2 + Re Yf() 1 ac ac Sf()=0 = 23 (4.3) YU0 3 Uf0t2π 11 Ni+−Re 2(1 +i )Re2 − Re 2 r ac 23ac ac
µ f = in which Reac = is the Reynolds number for periodic fluid flow and ft 2 is ft 2πρw a
defined as the transition frequency at which viscous ( ff< t ) or inertial ( ff> t ) fluid
forces dominate the fluid forces action on the cupula, here ρ and a is the density of the
Kaρw water and the acceleration of the canal flow; and Nr = is defined as the resonance 6πµ 2
factor, which governs the resonance properties of a cupula, µ is the dynamic viscosity of
the water.
4.2.3.3 Biomechanical Model for SNs
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Contrast to the CNs, SNs was driven by the external flow which is governed by the
boundary layer hydrodynamics over the surface of the body (Jielof et al 1952, Kuiper
1967, Hassan 1985, Kalmijn 1988, Dinklo 2005). McHenry and van Netten evaluated the
flexural stiffness of SNs in the zebrafish lateral line and found that the flexural stiffness is
proportional to the number of hair cells embedded in the cupula and the distal tip of the
cupula is predicted to be at least an order of magnitude more flexible than the proximal
region (McHenry and van Netten 2007). Consequently, they model the SNs as two joined
beams of different flexural stiffness, whose base behaves as a pivot that is coupled to hair
bundles that act as a spring (McHenry and van Netten 2007, McHenry et al 2008 and
Figure 4.2(b)). The structure is driven by the stimulus of an oscillating pressure field and
its boundary layer over a flat plate (McHenry et al 2008). Similar to the CNs, the
governing equation of motion for the cupula reads (McHenry et al 2008),
FzFzFzFzFzmeuab()+=++ () () () () (4.4)
Different from the governing motion equation for the cupula of CNs, the governing
equation is also a function of elevation z since the bending of the beam results in varying
forces at different elevations. On the left hand side, the spring stiffness term Fk in CNs model is replaced by the elastic stiffness term Fe(z) in the SNs model; and on the right
hand side, there is one more term defined as acceleration reaction force, Fa, due to the
relative acceleration of the flow and the cupula.
To evaluate the frequency response, a measure of sensitivity (McHenry et al 2008) is defined as the cupular deflection at the height of the tip of the tallest sterocilium, ν(hh), to
the free stream velocity, U0:
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ν (h ) ib ibωδ4 −(1 +ih) 3 ibω S (ω) ==−−h w 1 mmexp h +∑ Cexp izj 4 (4.5) νU0 j Uωδ b 4 j=0 EI 0 m 4EI+ iωδ bm
where Cj is a sequence of four integration constants;
hh is the height of the tip of the tallest sterocilium;
EI is the bending modulus of the neuromasts;
2 2 ikπµ bm=−−4πµ ki π( ρmw + ρ) d ω + ; L
ikπµ2 b=−−42πµ ki πρ d2 ω + ; wwL
L d = − =γ + k 2 , is the viscous drag coefficient with L ln( ) , where γ is L2 + (π /4) 2δ
Euler’s constant ( γ ≈ 0.5772 ), d is the diameter of the cupula and δ is the boundary layer
2µ thickness withδ = ; ρωw
ρw and µ are the density and dynamic viscosity of water, respectively; ρm is the density of the cupula matrix and ω is the angular speed of the stimulus.
4.2.3.4 Multi-layer filtering effect in CNs
Through modeling the responses of a CN or SN to their corresponding hydrodynamic environment, the sensitivity of the neuromasts in terms of their deflections to the flow
S S velocity ( YUc , νU0 ) can be analytically expressed as shown in Eq. 4.3 and Eq. 4.5.
Figure 4.3(b) and Figure 4.4(b) plot examples of the deflection responses to flow.
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Figure 4.3. Multiple-layer filtering of a CN to a vibrating sphere. (a): Illustration of the multiple-level
filtering of the CN system; (b): Theoretical modeling of the dynamics response of the CN: Thicker solid
line represents the sensitivity SY/a of CN deflection Y to the acceleration a of the flow in the surface of the
canal (left axis); The thinner solid line represents the sensitivity Sa/X of surface flow acceleration a to the
displacement of the vibrating sphere X (left axis); short dashes represents the sensitivity S of the canal Uac flow velocity to the surface flow acceleration (right axis); and long dashes represents the sensitivity S YUc
of the cupula displacement to the canal flow velocity (right axis). It can be seen that the flat low pass
response of S is the product of the low pass filter S and S ; (c) : The predicted sensitivity of Y/a Uac YUc
S , which is the product of S , S and S (Figure modified from Sane and McHenry 2009) Y/X Uac a/X YUc .
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However, complex filtering strategies were found in the flow sensing system in fish,
which is related to the propagation path of the external excitation as well as its
interactions with the sensory organ. Explorations of the filters can guide the sensor
design regarding to frequency response. Assuming a fish was exposed to a dipole
stimulus (vibrating sphere), which simulates an approaching prey activity, multi-layer
filters from the dipole source to the CN or SN response can be determined using
hydrodynamics and motion principles. This is elaborated in the following.
Figure 4.3(a) plots the propagation paths from the external excitation to CNs. In the first
stage, the sphere vibration produces pressure differences between the pores of the canals.
In the second stage, the pressure differences between the pores of the canals produce
canal flow. In the third stage, the canal flow deflects the CN and produces neural
responses.
The response function in the first stage, where sphere vibrating produces pressure
differences between pores of the canal, can be defined as the ratio of the surface
acceleration (a) to the vibrating amplitude of the sphere (X), noted as Sa/X. Sa/X can be easily obtained since the pressure field around a vibrating sphere is well understood based on the fundamental hydrodynamic theories (Stokes 1851; Harris and van Bergeijk
1962, Kalmijn 1988). With this theory, it can be derived that the acceleration of surface flow is proportional to the sphere’s acceleration and the sensitivity Sa/X is a linear
function of the stimulus frequency (Figure 4.3(b)).
The response function in the second stage, where the surface acceleration produces the
canal flow velocity, can be defined as the ratio of the surface acceleration to the velocity
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S S of the induced canal flow, noted as Uac . The sensitivity Uac can be analytically
resolved through theories for flow through cylindrical pipe (Sexl 1930, Denton and Gray
1982, 1983, 1989, van Netten 2006). Figure 4.3(b) plots the schematic of the response
function. As shown in Figure 4.3(b), the canal serves as a low-pass filter of the surface acceleration. The physical mechanism is at low frequencies, the viscosity dominates the resistance to the flow and the velocity of the canal flow is proportional to the surface acceleration; at higher frequencies, the inertial forces of the fluid reduce the velocity in inverse proportion to frequency.
The response function in the third stage, where the canal flow produces cupula displacement, can be defined as the ratio of the cupula displacement (Y) to the canal flow velocity (Uc), noted as SY/U. SY/U has been derived in Eq. 4.3. At low frequencies, viscous
drag dominates the fluid force on the CN cupula, CN cupula can be regarded as a flow
velocity sensor since the deflection of the cupula is in proportion to the velocity of flow
in the canal; at higher frequency, however, the inertial forces drive the CN to resonate,
causing an elevated sensitivity at such frequencies. Therefore, the interactions between
canal flow and cupula produces low pass filtering effects.
The combined canal and cupula filtering characteristics can be studied by employing a
new sensitivity function SY/a, which is defined as the ratio of the cupula deflection (Y) to
S S the surface acceleration (a) and is the product of YUc and Uac Eq. 4.6. The
combination of two low-pass filters is also a low pass filter (Figure 4.3(b)). Below the
S resonant frequency of the cupula, the cupula sensitivity YUc increases with frequencies
S while the canal sensitivity Uac reduces accordingly. The counter-acting trends of the
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two signals result in a constant sensitivity of the SY/a up to the cupula resonance
frequency (~115Hz), which indicates that the cupula can serve as an acceleration sensor
at the low frequency range, which makes it a good infrasound listener.
SSS= ⋅ Ya Ucc a YU (4.6)
The overall sensitivity SY/X, which is defined as the ratio of the cupula deflection (Y) to
the sphere amplitude (X), depends on the multi-level filtering effect from the sphere, canal, and cupula. This combination sensitivity can be calculated analytically as the
S S product of Sa/X, Uac and YUc (Sane and McHenry, 2009) Eq. 4.7 as well as measured neurophysiologically.
S=⋅⋅ SS S YX aX Ucc a YU (4.7)
Afferent recording of the response of CN (afferent action potentials) to vibrating sphere
agrees well with the predicted dynamics response (Figure 4.3(c)) at frequencies up to the cut-off frequency (Sane and McHenry 2009). This reveals the remarkable congruence of neurophysiology and biomechanics and indicates that the dominant factor for the CN is the mechanical properties of the CN.
4.2.3.5 Multi-layer filtering effect in SNs
The frequency response of the SN to flow-induced by different stimulus was studied by
researchers such as McHenry and his colleagues (McHenry et al 2008, Windsor and
McHenry 2009). The overall responses are decided by factors such as fields stimulus
hydrodynamics, the boundary layer and the fluid-cupula interactions.
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Figure 4.4. Multi-layer filtering of a SN to a pressure driven flow (b) and vibrating sphere induced flow (c).
In (a), the filtering mechanism is illustrated; and in (b) and (c): The sensitivity, S (thicker solid line, νU0
band pass), of the cupula deflection ν to the freestream U0 is a combination of the boundary layer filtering
effect (dashed line, high pass) and the flow structure interaction effect (thinner solid line, low pass); The sensitivity, S thicker solid line), of cupula deflection ν to the displacement of the vibrating sphere V , is νV0 0 a combination of the sphere induced boundary layer (dashed line, two-gain response) and the flow structure
interaction effect (thinner solid line, low pass). (Figure modified from McHenry et al 2008)
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Figure 4.4(a) plots the propagation paths from the flow disturbance to SN deflection. For
both near field spherical excitation and far-field free stream flow, the boundary layer plays an important role in determining the overall interactions between SN and copular responses.
S From local flow to SN deflection, the sensitivity νUh can be defined as the ratio of
deflection of the cupula at elevation of the longest stereocilia (ν) to the local flow velocity (Uh). The sensitivity can be estimated by modeling the SN cupula-flow
interaction. The responses are shown in Figure 4.4(b), 4.4(c). At low frequencies, the viscous forces dominate the hydrodynamic forces on the cupula and the cupula deflects in
S proportion to the local flow velocity, i.e. νUh is nearly a constant at low frequencies; at
higher frequencies, the acceleration reaction and inertia of the cupula dominates, and the
cupula deflects in proportion to the flow displacement. Thus, SN acts as a low pass filter
to the local flow.
As mentioned previously, the boundary layer plays an important role to the SN response.
The properties of the boundary layers (e.g. boundary layer thickness) are different due to
S different types of stimulus. To a pressure driven flow, the sensitivity UUh0(defined as
the ratio of the local flow velocity at the tip of the stereocilia, Uh, to the free stream
velocity, U0) can be regarded as a measure of these changes of boundary layer property.
S And UUh0can be obtained by the well-established hydrodynamic theory (Batchelor
1967, Schlichting and Joseph1979). The result show the boundary layer behaves as a low pass filter (with cut off frequency in the order of several thousand Hz).
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To a vibrating sphere induced oscillatory flow, the boundary layer between the sphere
and the skin where SNs are located is more complex. At low frequencies, the velocity
near the skin is large since the sphere carries a large volume of fluid viscously; at higher
frequencies, the vibration of the sphere reduces to a dipole source and the velocity is
3 rstimulus proportion to 3 , where rstimulus is the radius of the sphere and dstimulus is the distance dstimulus
S from the sphere. Thus, the sensitivity UUh0, which is the ratio of the local flow to the
velocity of the sphere, represents a two-gain response and has a greater sensitivity at
lower frequencies.
SS= ⋅ S νU0 U h0 U νU h (4.8)
SS= ⋅ S νV0 U h0 V νU h (4.9)
The overall sensitivities of the SN to the stimulus can be expressed as the ratio of the
S cupula deflection to the freestream velocity for pressure-driven flow (i..e, νU0 in Eq.
S 4.8) or sphere displacement for vibrating sphere induced flow (i.e., νV0 in Eq. 9). For
the pressure-driven flow, the combination of a low-pass filter (cupula) and a high pass
filter (boundary layer) results in a band-pass filtering effect, in which the boundary layer
S high pass filtering effect dominates the change of sensitivity νU0 at low frequencies. For
the sphere induced flow, a cupula is most sensitive to the oscillations of a sphere at low
frequencies and the sensitivity attenuates throughout the frequency range. For larger
diameter spheres, there exists a flat response region in the low frequency range, which is
due to the influence of the boundary layer between the skin and the sphere.
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From the above discussions, it’s clear that the sensitivity of a CN mainly depends on the
canal hydrodynamics and the fluid-cupula interaction; while the sensitivity of a SN,
depends critically on the stimulus hydrodynamics, the boundary layer, and the fluid-
cupula interaction. The variations in morphology of CNs and SNs in aquatics may imply
that such variations enable them to be sensitive to a wide range of frequencies.
Analogically, a proper design of the morphology of individual artificial neuromasts may
tune the whole sensing system to a wide bandwidth.
4.3. BIO-MIMICKING: ARTIFICIAL HAIR FLOW SENSORS
Through the review on the biological hair flow sensors in the previous context, we learn that the aquatics and arthropods are enabled to not only “feel” the flow, but also “listen” to particular frequency bands, and filter noisy or unwanted signals. This capability is all attribute to the hair or hair-like structures, which have attracted a lot of interest from researchers to construct artificial counterparts. In this section, we try to provide a state- of-knowledge review on the development of bio-inspired hair flow sensors, including the design, fabrication, performance and packaging of such sensors. Comparisons are also conducted on these sensors and discussions are delivered. The review is restricted to the mimicking of the high aspect-ratio hair-like sensing structures. MEMS flow sensors with high spatial and temporal resolutions have also been designed and fabricated, however, without mimicking the high-aspect-ratio hair-like structures. This is beyond the scope of this Chapter and the readers are referred to Chen et al (2007) for further information.
Based on the sensing principles or readout mechanisms, the biomimetic hair flow sensors are categorized into several groups, namely, thermal, piezoresistive, capacitive, magnetic,
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and optical sensors. Flow sensors based on thermal principle such as Hot-Wire
Anemometry (HWA) are well-studied and commercialized in the past decades. In such sensors, a thermal element serves both as a heater and a temperature sensor when in operation. The temperature of the thermal element will change when flow passes it and
the changes of temperature indicate the cooling rate and the flow velocity (Chen et al
2003). An array of MEMS HWA was studied recently for hydrodynamic object tracking
or underwater dipole localization and such a system was termed as an artificial lateral line
system (Chen et al 2006a, Pandya et al 2006, 2007, Yang et al 2006, 2010). Although at
the level of array layout, it mimics the lateral line system, at the level of single sensors, it
shares few common properties with biological hair sensors due to the disparate sensing
principles. The detailed description of the single HWA sensor are not duplicated here and
the array level processing algorithm of such arrays are discussed in the next section.
MEMS based biomimetic flow sensors were also briefly reviewed by Zhou and Liu
(2008). In this section, we discuss in detail the bio-inspired hair sensors based on
different sensing principles. Biomimetic hair flow sensors (BHFS) sensors based on the
piezoresistive and capacitive principles are among the most mature sensors and therefore we discussed these types of sensors with great details. Biomimetic hair flow sensors with other read-out systems are also briefly reviewed in order to inspire further interests in such areas.
4.3.1 Piezoresistive BHFS
Piezoresistive sensing is commonly used in engineering and the most common case is the piezoresistive strain gauge. The mechanical deformation can be measured by the change
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∆Rp of electrical resistance of the piezoresistive sensor ( ∝ ε , where Rp is the electrical Rp
resistance and ε is the strain). Artificial hair flow sensors with different designs are fabricated and characterized by the MedX Lab in Northwestern University under the
DARPA BioSenSe program. Their designs are mostly inspired by hair cells in nature
(reviewed by Liu 2007 for their previous achievements), especially the neuromasts in the
lateral line system.
Three components constitute the functional structure of the piezoresistive BHFS from the
MedX Lab: a vertical hair-like structure, an in-plane cantilever and a silicon resistor
(Figure 4.5). The principle of the piezoresistive BHFS is straightforward: the hair
structure rigidly connects at the far end of the cantilever; flow induced drag forces drive
the hair shaft to deflect; the moment transfers to the lateral cantilever, which deflect
simultaneously with the hair shaft; the deformation at the base of the cantilever can be
monitored using the piezoresistor. The deformation induced changes of resistance can be
easily measured with an on-chip or external Wheatstone bridge.
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Figure 4.5. Piezoresistance based MEMS hair sensors from the MedX Lab. Schematic drawings of the first
design (a), second design (b) and third design (c) of a single sensor, and the corresponding SEM pictures
(d), (e) and (f), respectively. The hair of the first design was made of metal or metal/Permalloy, and was
replaced with SU-8 hair in the second design. A layer of hydrogel “cupula” covered the SU-8 hair to form
the sensor of the third design. Figures are adapted from Fan et al 2002 (a and d), Nguyen et al 2011 (b),
Yang et al 2011 (e), Peleshanko et al 2007 (c) and McConney et al 2009b (f).
The MedX Lab proposed three different designs of the BHFS utilizing different materials
and different fabrication methods for the hair structure (Figure 4.5). In the first design
(Figure 4.5(a), (d)), the vertical cilium is made of a gold-Permalloy composite and realized using a three-dimensional assembly technique called plastic deformation magnetic assembly (PDMA). The piezoresistor and the lateral cantilever beam were fabricated using doping and etching techniques, respectively. Before the PDMA process, a sacrificial layer of copper and a thin layer of gold are deposited and patterned using photolithographic methods, followed by a deposition of the layer of Permalloy material.
The copper layer is then removed with diluted HCl solutions and the freed gold-
Permalloy composite cantilever is exposed to a high magnetic field. The cantilever is then
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rotated off the substrate due to the magnetic force. Plastic deformation of the gold ensures that the cantilever remains at a certain angle (e.g. 90°), which can controlled by choosing certain geometry of the cantilever and the magnetic field. To define a specific bend region and reduce the stress concentration at that region, the electroless plating method is used to enhance the bend region. This treatment leads to a significant yield of assembly. The fabricated device is also coated with a uniform Parylene layer for strengthening and electrical insulation (Li et al 2002, Fan et al 2002). To increase the robustness of the device, polymer substrate is used instead of silicon (Chen et al 2003). In the latter design, the vertical hair is rigidly attached to the substrate, the lateral cantilever is omitted and the strain gauge is attached at the base of the hair. The vertical hair is also realized using the PDMA process and the difference is that the cantilever is based on a layer of polyimide (Chen et al 2003) instead of silicon. The details of fabrication and performance of the MedX Lad’s first design of the MEMS hair flow sensors are also reviewed by Nawi et al (2011).
In the MedX Lab’s second design, the hair structure is made of SU-8 and the circular high-aspect-ratio SU-8 hairs are realized using spin process and photolithography methods (Figure 4.5b, e). In fact, PDMA process is based on the surface micromachining, which limits the structure to be asymmetric (e.g. rectangle in the first design). Therefore the MedX Lab’s first design poses limitation on the spatial resolution. In its second design, the spatial resolution is improved since the hair structure is in a symmetric circular shape. The piezoresistors and the corresponding on-chip Wheatstone bridge resistors for the second design are achieved by ion implantation. After the vertical hair assembly, the devices are released in buffered oxide etch to free the lateral cantilever
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(Chen et al 2006b, 2007, Tucker et al 2006). In the whole fabrication process, the SU-8
step is the only step which is not standard since the SU-8 is very sensitive to processing parameters; however, the SU-8 process minimized manual handling of the devices during fabrication and thus improves the yield and enables array fabrication (Chen et al 2006b,
2007).
In the MedX Lab’s third design, artificial cupula is fabricated to encapsulate the SU-8
hair. As described in the previous review, for the neuromasts in the lateral line system,
the cupula plays an essential role in the sensitivity of the neuromasts. The cupula is very
flexible in nature (McHenry and van Netten 2007) and it couples the neuromast hairs to
the surrounding hydrodynamic environment maximizing and mediating drag forces
(Peleshanko et al 2007). Inspired by the cupula of neuromasts, a combined hybrid soft-
hard material design of the micro-flow-sensor is introduced and hydrogel cupula grown on the SU-8 hair of the second design is realized by wet-chemistry micropatterned photopolymerization method (Peleshanko et al 2007). The key process of the cupula encapsulation includes the spreading of the water-soluble polyethylene glycol (PEG) monomer, the patterned photopolymerizing through UV photo-crosslinking, the removing of the non-reacted monomer layer and the swelling of the PEG layer using water
(Peleshanko et al 2007). The achieved cupula using this technique is in dome-shape and extends the SU-8 hair by 30%-40% in height and by 10-20-fold in diameter. In order to achieve high-aspect-ratio cupula, which mimics the superficial neuromast cupula, an alternative approach is utilized. Droplets of poly(ethylene glycol) tetraacrylate (PEG-TA) are dispensed from a syringe and manually deposited on to the SU-8 hair. The realized cupula starts from the midpoint of the SU-8 hair and extends the hair by 50%, which is a
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good balance between robustness, height and preventing wetting of the platform
(McConney et al 2009b). The elastic modulus of the artificial cupula is within 8-10kPa
(Peleshanko et al 2007) or of the order of 10Pa (McConney et al 2007), which is similar to their biological counterparts.
Systematic characterization of the MedX Lab’s piezoresistive flow sensors showed high flow sensitivity and angular sensitivity both underwater and in-air (Chen et al 2007). The gauge factor of the second design can reach 33.6 to 78.9 (Chen et al 2006b, 2007). The sensitivity of 100mm/s in water tunnel is reported for the first design (Fan et al 2002); the sensitivity is increased to below 1mm/s in water (0.1mm/s is also reported by Tucker et al
2006) for the second design (Chen et al 2007); with the artificial cupula the sensitivity is further increased by 10-fold to 40-fold (Peleshanko et al 2007; McConney et al 2009b).
This sensitivity is compatible with that of neuromasts of lateral line system. The off-axis rejection ratio in the second and third designs is as high as approximately 17.5:1, which shows a high degree of directional sensitivity (Chen et al 2007). Wind tunnel directionality test demonstrates a clear “figure of eight” sensitivity pattern on the polar plot and the angular resolution of 2.16° in the air is achieved (Chen et al. 2007).
Besides the group mentioned above, there are also several groups who take the advantage of piezoresistive principle to mimic the functions of biology hair flow sensors. Ozaki et al (2000) proposed two types of air flow sensors inspired by the wind receptor of insects.
Both designs applied the piezoresistive principle. Their 1-DOF sensor consists of an array of planar cantilevers with strain gauges on the base and the 2-DOF sensor consists of a cantilever fixed on a cross-shaped beam with strain gauges in each direction. The same principle with the Ozaki’s 1-DOF sensor was also adopted by Wang et al (2007), Zhang
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et al (2008), Du et al (2009), Aiyar et al (2009) and Song et al (2011), Qualtieri et al
(2011). The differences of such sensors lie in the material and machining techniques, geometries and the sensitivity. The principle of Ozaki’s 2-DOF sensor was also employed by other researchers (Xue et al 2007, Zhang et al 2008 and Wang et al 2008).
Table 4.1 provides a summary to compare the fabrication and performance of these different sensors. All these designs adopted symmetric or circular cantilevers and enables the capability for bi-directional flow sensing benefiting from the four orthogonally arranged piezoresistive strain gauges. Among these designs, some of them are not designed for flow sensing but for tactile sensing (Engel et al 2005, Hu et al 2010) or pressure sensing (Xue et al 2007 and Zhang et al 2008), but they also have potential to be redesigned as flow sensors. It is worth noting that some of these sensors are all-polymer based, and showed the capability to use flexible substrate or to be integrated with flexible
PCBs (Engel et al 2005, Aiyar et al 2009 and Song et al 2011).
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Table 4.1. Summary of Different Designs of Piezoresistance Based MEMS BHFSa.
Design Piezoresistance Hair Material Hair Method Hair Geometryb Note
Material
MedX Lab 1st (Fan Boron Ion Diffused Si Metal/Polymer- PDMA 820-1100µm *100- Sensitivity: 100mm/s
et al 2002) Permalloy 200µm *10µm
MedX Lab 2nd Boron Ion Diffused Si SU-8 Photolithography 600µm* φ80µm Sensitivity: 0.1mm/s
(Chen et al 2007)
- rd 136 MedX Lab 3 Boron Ion Diffused Si SU-8-Hydrogel PEG deposition/photo- dome : 500-1000µm Sensitivity: 75µm/s -
(Peleshanko et al crosslinking *φ1000-2000µm; (dome)
2007, McConney et High aspect-ratio: 2.5µm/s (high-aspect-
al 2009b) 800µm*φO(100µm) ratio)
Ozaki 2DOF Boron Ion Diffused Si Wire of unknown Manual bonding 3000µm *φ500 µm Range: O(0.1)m/s -
material 2m/s
Engel et al 2005 Carbon-impregnated Polyurethane Micro-molding 3000µm orthogonal Used as Tactile
Polyurethane Sensor
Xue et al 2007 and Boron Ion Diffused Si Rigid Plastic Manual Bonding 5000µm*200µm Used as Hydrophone
Zhang et al 2008
Wang et al 2008 Platinum NA NA NA Range: 15-30m/s
Hu et al 2010 Polysilicon Silicon Post Etching ~3000µm*320 µm Used as Tactile
Sensor
Ozaki 1DOF Boron Ion Diffused Si Silicon Nitride Etching 400-800µm *230 µm Range: O(0.1)m/s -
2m/s
Wang et al 2007 Platinum Silicon Nitride Etching 4000µm *400-2000µm Range: 5m/s-45m/s - 137 Du et al 2009 Platinum Silicon Nitride Etching 3000µm *2500µm Range: up to 18m/s -
Aiyar et al 2009, Elastosil® Kapton® Laser Planar 1500µm*400µm Range: up to 16.9m/s
2011 micromachining
Zhang et al 2010 Sillicon Silicon dioxide Dry etching 100-400µm*20- Range: 0-0.2m/s
40µm*0.8µm
Qualtieri et al 2011 Aluminum Nichrome alloy Etching 200-600µm*100µm
Ni/molybdenum
aThe geometries appeared here are only for the sensors appearing in corresponding literatures. The techniques are not limited to such geometries, though.
b The geometry is expressed by a product : length*width (or radius) (*thickness)
4.3.2 Capacitive BHFS
εm A Capacitive readout ( C = , where C is the capacitance, εm is the permeability of the d//
medium between two parallel plates, the d// is the distance and A is the overlapping area)
is widely used in many different types of sensors due to its high sensitivity and low
power dissipation (for designs and applications of capacitive sensors, the readers are
referred to Baxter 1997, Ghafar-Zaheh and Sawan 2010). Several research groups have
developed sophisticated BHFS prototype based on capacitive principle.
The Transducers Science and Technology group within MESA+ Institute for
Nanotechnology in University of Twente, Netherlands is one major player in developing
capacitance-based artificial hairs inspired by cerci of crickets. Several designs of
BHFS/array with high sensitivity have been fabricated using advanced MEMS techniques.
The characteristics of different designs are the improvements in its geometry
optimization and fabrication processes. The detailed fabrication processes are not
elaborated here. Only the principle of operation for these sensors is briefly described.
In Twente’s designs, each artificial hair is situated at the center of a suspended membrane and a capacitor is formed by the top electrodes which are deposited on the suspended membrane and the bottom electrode on the base of the substrate. A schematic drawing of such sensors is illustrated in Figure 4.6(a). Flow induced tilting of the hair is resisted by the torsional stiffness of the membrane, whose deflection will result in the change of the capacitances of the sensor.
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Figure 4.6. The schematic drawing of the capacitive hair sensors (a) and an example of fabricated sensor
array (b). The hair is made of SU-8, which can be coated and exposed as multiple layers; the membrane
and the wafer bottom form a variable capacitor. Figures are adapted from Bruinink et al 2009.
In Twente’s first sensor design (van Baar et al 2003), the hair is made of SixNy and the membrane is suspended either with spirals running around or with the so called double- gimbal suspension consisting of orthogonal torsional springs (Figure 4.7(a)). The fabrication is monolithic and is realized through a combined bulk/surface micromachining process (van Baar et al 2003).
Figure 4.7. Different designs of capacitive hair sensors: The first design was monolithically fabricated and the hair was made of SixNy (a); from the second design (van Baar et al 2003) (b) on, the hairs are made of
SU-8; the membrane is fully supported and made of SU-8 in the third design (Dijkstra et al 2005) (c),
which is different from the other designs (Izadi et al 2010); In the fourth design (d), the bottom electrode
are fabricated separately using SOI (Silicon-On-Insulator) technique (Dagamseh et al 2010a )
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In Twente’s later design, the sacrificial poly-silicon based read out structures, i.e., the
membrane capacitors are first fabricated using surface micromachining technologies and
the hair structures are realized through illuminating a layer of SU-8 photoresist, which is
previously spine-coated on the top of the membrane structure (Figure 4.7(b), Dijkstra et
al 2005). Using multiple layers and multiple exposures of SU-8 can increase the hair length up to and above 1mm with several segments stacked on each other (Krijnen et al
2006). In order to eliminate the curvature effect of the membrane due to the tensile stress
in the electrodes thin layer (Chromium), the electrode thickness and length are reduced to
obtain maximum sensitivity (Izadi et al 2007a,b). Further modifications of several parts
of the flow sensor such as the hair length, the inter-electrode gap, the membrane shape
and torsion beam geometries result in 100-fold increase in sensitivity to capture the flow
amplitude in the order of 1mm.s-1 (Bruinink et al 2009, Jaganatharaja et al 2009). We call
such designs as the Twente’s second design of the capacitive BHFS.
To extend the sensors to liquid flow, the capacitive sensors are further refined to
Twente’s third design. In this design, the torsional SixNy membrane is replaced with fully
supported flexible SU-8 thin membrane and the electrodes are insulated from liquid to
prevent short circuit (Figure 4.7(c), Izadi et al 2010).
In the first three designs of capacitive sensors, an array of hairs shares a common bottom electrode and thus prevented the wafer-scale array addressing. To enable fabrication of independent sensing electrodes, the Silicon-on-Insulator (SOI) wafer technology was utilized (Figure 4.7(d)). This enables individual array element measuring and the
Frequency Division Multiplexing (FDM) is interfaced to realize array addressing
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(Dagamseh et al 2011). This design is termed as the Twente’s fourth design of the capacitance based hair flow sensor.
The response of the capacitive sensors can be modeled as a three-tier system consisting of
the mechanical system of the torsional suspended hair, the aerodynamic system and the
capacitive transducer system (Krijnen et al 2007b). The performance of the sensors is
evaluated by the figure of merit (FOM), which is defined as the product of usable
bandwidth and sensitivity. It is showed that in order to obtain a high FOM, long thin hair
made of low density with small torsion stiffness is required. Although the authors
mentioned that combining many hairs with different geometries would create a sensitive
sensory system with relatively balanced frequency spectrum (Krijnen et al 2007b), none systematic analyses on this topic have been conducted. Instead, the researchers focus on the electrostatic spring softening effect by DC-biasing or AC-biasing in order to adaptively change the effective properties of the sensors (Krijnen et al 2006, Floris et al
2007, Wiegerink et al 2007, Izadi et al 2007a,b, Krijnen et al 2007a, Droogendijk and
Krijnen 2010, Droogendijk et a. 2011, Droogendijk et a. 2012). Based on the capacitive
transduction theory, both the effective spring stiffness and the resonant frequency of the
sensor will decrease with increasing bias voltage (Wiegerink et al 2007, Krijnen et al
2007a).
Table 4.2 summarizes the major characteristics of capacitance-based BHFS from this
group.
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Table 4.2. Summary of Different Designs of Capacitance Based BHFS developed by the group in Twente
Hair Designs Electrodes Membrane Sensitivity Sturcure
st Spiral & 1 (van Baar et al 2003) SixNy Common torsional --
2nd (Dijkstra et al 2005, Spiral & SU-8 Common O(1mm/s) in air Bruinink et al 2009) torsional
rd Fully 4*10-3 rad/(m.s) at 3 (Izadi et al 2010) SU-8 Common supporteda 115Hz in air
4th (Izadi et al 2011) SU-8 Separated Torsional --
aMembrane made of SU-8
The directionality and the sensitivity of the sensors to acoustically-induced air flow have also been characterized. Experiments revealed that the output of the sensor displays a figure of eight and the sensor has a preferred direction of sensitivity (Dijkstra et al 2005,
Krijnen et al 2006, Jaganatharaja et al 2009, Bruinink et al 2009, Dagamseh et al 2010a).
The sensitivity to oscillating air flow is down to the order of 1mm/s (Bruinink et al 2009).
A sensitivity of 0.85mm/s is also reported at 1kHz operational bandwidths (Jaganatharaja
et al 2009).
Capacitive sensing principle was also employed by Stocking et al (2010) to develop a
whisker-like artificial sensor mimicking seal vibrissae. In their design, the capacitors are
not of the common flat parallel plates but of a cone-to-cone shaped parallel-plate, which is separated into four distinct quadrants. It also has a membrane structure providing damping and restoring forces. The sensor is in macro-scale with the diameter and the length of 4cm and 2mm, respectively, which is in the same scale as the seal vibrissae.
Barbier et al (2008) designed a capacitive based hybrid flow sensor with a flexible base supporting a whisker-like epoxy hair. The flexible membrane takes the features of spider
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trichobothria and the hair is larger in size. A recent study employed the gel-supported
lipid bilayer as the base of the hair and the flow induced vibration of the hair can produce
currents due to the time-varying change of capacitance of the membrane (Sarles et al
2011a, c). This work advanced the bio-inspiration to a new stage that not only mimicking
flow sensing function of hair/hair-like structures, but also mimicking the biology membrane structures to realize such functions.
4.3.3 BHFS based on other principles
BHFS based on other sensing principles such as optical, and magnetic ones have also been explored by different researchers. Although most of them are only in the starting stage or restricted in pilot laboratory research only, principles of such design are reviewed here to inspire further investigation.
An optically-based artificial lateral line canal was built with artificial canal neuromasts inside to determine object positions, vortex shedding frequencies and flow velocities
(Klein and Bleckmann 2011). The bending of transparent silicone bars, which served as the hair, was detected optically with the use of LED, optical fibers and photo transistor.
The light from LED travels through the transparent bar and illuminates the optical fiber at the opposite end of the bar. The light then is received by the connected photo transistor, which provides the output. Several canals with different diameters and different numbers of pores are fabricated and are applied to the detection of various hydrodynamic phenomena. Another application of the optic principle and micro pillar for hydrodynamic measurement is the development of microstructured surfaces for shear stress mapping
(Brucker et al 2005, 2007, Grosse et al 2008) or for nano-newton drag sensing (Grosse et
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al 2006). These surfaces consist of arrayed micro-pillars made of PDMS through micro- molding. The diameters of such flexible pillars are in the order of 10µm and the aspect-
ratio reaches to 10-20. Since the pillars are well situated in the boundary layer of
interested viscous flow, it is feasible to retrieve the near wall shear stress based on the tip
deflection of the pillar, which is recorded using a high-resolution camera. Such micro-
pillars also have the potential to be utilized to obtain other hydrodynamic characteristics
such as the velocity field and turbulence intensity.
Applications of magnetic materials in acoustic sensing inspired by cilia of the human ear
and its potentials for flow sensing are found in recent studies (McGary et al 2006,
Downey et al 2008 and Biju et al 2011). Newly developed magnetostrictive alloy
Galfenol (Fe1-xGax0.1≤x≤0.25 at. %) wires in nanometer scale presents excellent
magnetostrictive effect and perform well in the bending regime and thus was proposed as
a candidate material for acoustic sensing (McGary et al 2006). The bending induced change in magnetization of the nanowire is detectable either using a pickup coil of
AWG34 magnet wire or a GMR sensor (Downey et al 2008).
4.4. ON THE METHODS FOR INFORMATION PROCESSING
At the level of information processing, biologists, neurologists and engineers are all
involved to unveil the processing mechanism for aquatics or arthropods to encode and
decode the hydrodynamic information. In recent years, scientists have physiologically
identified the peripheral steps in the lateral line signal transduction (Dijkgraaf 1963,
Bleckmann and Zelick 1993, Coombs et al 2000, Coombs and van Netten 2006); the
hydrodynamic and mechanical properties of individual neuromasts have been modeled
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(see Section 2); preliminary study has also been conducted to try to retrieve the simple
hydrodynamic information induced by simple hydrodynamic stimuli such as a dipole
source (Coombs 2001,Curcic-Blake and van Netten 2006, Chagnaud et al 2007b, Goulet
et al 2008), by more complex stimuli such as objects passing the fish laterally
(Bleckmann and Zelick 1993, Mogdans and Goenechea 1999, Müiler et al 1996, Plachta
et al 2003), by fish heading to or gliding parallel to a wall (Windsor et al 2010a, b), by
vortices and in running water (Engelmann et al 2002, Chagnaud et al 2006, Chagnaud et
al 2008a) and by Karman streets (Chagnaud et al 2007a, Akanyeti et al 2011). The
details of the peripheral and central processing of the lateral line information are beyond
the scope of this review and the readers are referred to Bleckmann (2008) for a
comprehensive review. Here we just highlight several hypotheses.
To locate a dipole source, one hypothesis is based on the linear relationship between
spatial variation in pressure gradient (thus the spatial variation in CN response) or
velocity field (thus the spatial variation in SN response) and the dipole source distance. In
this algorithm, the dipole distance dstimulus can be linearly related to the distance between
Szeros zeros Szeros( dstimulus = ) or between maxima and minima Sextreams( dSstimulus= extreams ) 2 of the velocity field. It was first proposed by Franosch et al (2005) and the algorithm is also testified experimentally by Curcic-Blake and van Netten (2006) and Goulet et al
(2008). Curcic-Blake and van Netten (2006) proposed a potential decoding algorithm that
might be used by fish to reconstruct the quantitative mapping of dipole source positions
and the directions of vibration through the continuous wavelet transform technique,
which is a relatively complicated mathematical procedure; Goulet et al (2008) further
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suggest that the superficial and canal neuromasts employ the same mechanism and the
simple linear relationships are enough to retrieve the dipole location directly and
straightforwardly. Chen et al (2006a) and Dagamseh et al (2010b) applied this method to
locate a dipole source using the hot wire anemometer based and capacitance based flow-
sensor array, respectively.
Another hypothesis is based on the time delay between response signals of two
neuromasts. Bleckmann and co-workers studied the lateral line responses of fishes in
both still and flowing water. They found that the response of SNs to the vibrating sphere
induced fluctuations in flowing water was masked (Engelmann et al 2002) and an
increased response to flow rates occurred even if flow direction was reversed (Chagnaud
et al 2008a). Therefore, they concluded that individual lateral line nerve fibers encoded
neither the flow velocity nor the flow direction; they suggest that higher order neurons
can retrieve the flow information, however, through at least a pair of neuromasts
(Chagnaud et al 2008a). They proposed a cross correlation algorithm to determine the
time delay between responses of two neuromasts induced by a same structure passing
them in a turbulent bulk flow and the hypothesis is experimentally supported (Chagnaud
et al 2008b). Given an array of neuromasts and the time delay between the responses, the
bulk flow velocity can then be easily determined. A similar delay-line hypothesis is also proposed to interpret the information processing of the crickets cercal system (Mulder-
Rost et al 2010). This algorithm is also used in an optical artificial lateral line system to
determine the velocity of the bulk flow (Klein and Bleckmann 2011).
The directional information retrieved from the filiform hairs in the crickets are studied
mainly using the tuning curve technique, which determines the input-output relationship
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defined by the function relating the values of the stimulus parameter to the measured output of the cell, or vice versa (for details, see the review by Jacobs et al 2008). Another hypothesis for the direction detection is that crickets may perceive the direction information of the incoming flow benefiting from the high-density nature of hair flow sensors all around their entire cerci, and from the frequency decomposition capability due to variable lengths of the hairs (Steinmann et al 2006).
When studying the information transfer and processing in the biological sensory systems, the effect of noise has also drawn researchers’ attention. In a linear system, the addition of noise will degrade detectabilities (Moss, 1994); in a nonlinear system with a threshold, however, the addition of an optimal level of noise to a weak information-carrying stimulus can enhance the information content at their outputs and improve the output signal to noise ratio (Douglass et al 1993, Levin and Miller 1996, Russell et al 1999 and
Moss et al 2004). This phenomenon is called stochastic resonance (for a review, see
Moss et al 2004). Stochastic resonance (SR) has been experimentally observed in predator avoidance for crayfishes and crickets based on the perception of flow motion: it was reported that the information transfer in crayfish mechanoreceptors (sensitive hairs on the tail fan) is enhanced by the presence of optimized, random noise (Douglass et al
1993); SR has also been established in the experiments on the cercal system of crickets which is capable of detecting small-amplitude low-frequency air disturbances (Levin and
Miller 1996). It is worth noting that the stimuli in the former experiment was periodic with a single frequency, whereas in the latter experiments the cells were subjected to broad-band input signals and thus demonstrating broadband SR or aperiodic SR.
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All the above mentioned hypotheses have implications for the artificial intelligence for
biomimetic hair sensor arrays. On the other hand, novel algorithms developed for
artificial hair sensors may also have implications for the information processing of
biological hair sensors. Algorithm based on the maximum likelihood estimator is
developed for dipole source localization and later, a more sophisticated algorithm
applying the adaptive beamforming (Capon’s method) technique was developed to
visualize flow disturbances in conjunction with a hot wire anemometer based artificial
lateral line system (Pandya et al 2006, Pandya et al 2007 and Nguyen et al 2008). The later one has a higher spatial resolution. In such algorithms, two branches of data are constructed. One is the experimental branch with data collected using the artificial lateral line; the other is the analytical branch with data from dipole velocity model. Matching of these two branches can be achieved through systematically scanning through all possible dipole states and the best matching is evaluated either by minimum-squared error algorithm (Pandya et al 2006) or by the adaptive beamforming algorithm (Pandya et al
2007 and Nguyen et al 2008). The latter algorithm is also applied to determine the dipole source location or to track a source with a piezoresistance-based artificial lateral line
(Yang et al 2007a, b, Yang et al 2010, Nguyen et al 2011) and a capacitance-based flow sensor array (Dagamseh et al 2011). Abdulsadda and co-workers (2011) applied an
artificial neural network to process the signals acquired by their ionic polymer-metal
composites (IMPC)-based artificial lateral line. The neural network is based on the
multilayer perceptron (MLP) architecture which is a widely used network structure to
solve nonlinear classification and prediction problems. In this MLP architecture, the
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sensor signals (input layer) are processed through a specific learning procedure (hidden
layer) to retrieve the dipole source location (output layer) (Abdulsadda et al 2011).
Although various hypotheses exist, our knowledge about the information processing in
biological hair sensor systems is limited and further research involving biology and
neuroscience are still required to unveil the mystery.
4.5 SUMMARY
In summary, the natural flow sensors in the biology world are an enormous inspiration source for artificial hair flow sensors. Comprehensive understanding of the biological sensing systems including their sensing ability, the sensing components and sensing principles, and the characteristics influencing their sensitivity such as geometries and distributions can help develop artificial counterparts and assist the design of biomimetic flow sensors. Such knowledge will also shed light on the biological and ecological mysteries in terms of the adaptive advantage of such sensing mechanisms. Biologists, neuroscientists and engineers have to work together to unveil the flow sensing mechanisms of the biological hair flow sensors and to develop artificial counterparts with similar and even better performance.
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CHAPTER 5
INNOVATIVE BIO-INSPIRED HAIR SENSORS BASED ON
PIEZOELECTRIC MICROFIBERS
5.1. INTRODUCTION
In Chapter 1 and Chapter 3, the importance of turbulence on the scouring process is illustrated. This chapter is dedicated to the design, modeling, optimization and fabrication of innovative bio-inspired hair sensors for turbulence measurements. The functional component of the sensors is an emerging smart material: piezoelectric microfibers.
Different from the piezoresistance material whose electrical resistance will change due to applied stress or strain, piezoelectric material generates charges when experiencing mechanical load or deformation. On the other hand, if the material is exposed to an external electrical field, it will deform. Such properties make piezoelectric material to be widely used as a smart element for sensors, actuators and even energy harvesters.
Recently, PVDF micro/nano fibers are fabricated using a novel method called thermo- direct drawing procedure (Liu et al 2008, Li et al 2010). The fibers can be produced to be suspended and aligned on insulator films. After fabricating electrodes along the drawing direction and poling under high voltage, the fibers are responsive to pressure stimulations.
The potential of such fibers in flow speed measurement is validated in a preliminary study. However, the fibers are suspended in plane and cannot benefit from the nature of the out-of-plane design of biological hair flow sensors. Besides the direct piezoelectric effect which the aforementioned piezoelectric based flow sensors utilized, piezoelectric
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material can also be used as a measure of frequency. Jing et al (2010a, b) designed a
MEMS flow sensor in which a silicon beam stands on a thin layer of PZT diaphragm.
The flow induced strain on the bending beam, producing stress on the diaphragm. The stress increased the stiffness of the diaphragm and thus changed its resonant frequency. If the standing beam was integrated with a PZT layer itself, the resonance frequency shifting effect induced by flow-induced vibrations could also be monitored (Kim et al
2009a, b). The resonant frequency of the diaphragm or the standing hair could be obtained either by excitation of an external alternating current (Jing et al 2010a, b), or by
Fourier transform of the time-varying signal (Kim et al 2009a, b).
5.2. PIEZOELECTRIC MICROFIBER BASED HAIR SENSOR WITH SURFACE ELECTRODES
5.2.1. Sensor design and computer modeling-assisted performance analysis
Figure 5.1 shows the schematic of the design of the hair sensor element to emulate the directional responses of natural hair cells in fish otolith. The sensor element features a simple geometry with a piezoelectric microfiber and one pair of surface electrodes. The piezoelectric micro fiber is coated with a symmetric pair of electrodes separated by gaps.
PZT microfiber is an emerging type of smart material that allows for flexible integration into various sensing elements (Bent and Hagood 1997). Different designs of patterning the electrodes on PZT microfiber composites have been proposed for sensing or actuating purposes (for example, Bent et al., 1999; Tan and Tong, 2001). It is the first time to fabricate a pair of opposite cylindrical surface electrodes on a single PZT microfiber.
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Figure 5.1. Schematic drawing of the proposed sensor. (The sensor consists of a piezoelectric fiber coated
with a pair of separated electrodes; the deformation of the fiber generates charges, which can be collected
and recorded through the electrodes. The directions 1,2,3 are used in the subsequent discussions in this
paper.)
As mentioned earlier, the piezoelectric microfiber in our design serves not only as the shaft mimicking the biological hair sensors, but also as the transduction element which converts the stimulations to electrical signals. When a piezoelectric fiber is stimulated by contact forces, fluid induced pressure differences or acoustic waves, and the deformation of the fiber produces charges on the surface due to the piezoelectric effect of piezoelectric material. Electrical charges with different polarities concentrate on different areas depending on the nature of strains (i.e. tensile or compressive); this results in an electrical potential difference. Through the pair of electrodes, such an electrical potential difference can be measured and recorded. In this section, the transduction behaviors of the newly designed PZT fiber, especially the directional sensitivity, are studied using a simplified analytical model and a finite element numerical model, respectively.
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5.2.1.1. Simplified analytical model of sensor transduction behaviors
The sensitivity or the effectiveness to convert mechanical deformation to electrical output
of such a design is dependent upon the polarization status of the piezoelectric material.
According to piezoelectric theory, the equations for the piezoelectric effect can be
expressed as in Eq. 5.1 (Ikeda 1996).
S= sE T + dE T (5.1) D=ε E + dT
In Eq. 5.1, S and T are the mechanical strain and stress, respectively; D and E are the
electric displacement and electric field, respectively; sE is the elastic compliance tensor in
condition of constant electric field and εT is the dielectric permittivity in condition of
constant stress status; and d is the piezoelectric coefficient.
To simplify the analytical model, the piezoelectric effect is uncoupled and the generated
charges displacement (D) is assumed to be only related to the applied strain ε through piezoelectric constant d, as shown in Eq. 5.2.
3 Dd=⋅ε=∑ d3ii ⋅≈ εε d31 ⋅ 1 (5.2) i=1
where d3i is the piezoelectric coefficient constant for the induced polarization in direction
3 (parallel to the direction in which the piezoelectric fiber is polarized) per unit stress applied in direction i. The first subscript of the piezoelectric constant d3i indicates the
initial polarization direction, and the second subscript denotes the direction of the applied
force.
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In the current design, the fiber is polarized with the surface electrodes and therefore the
initial polarization direction 3 coincides with the y direction (Figure 5.2). For a cantilever
exposed to transverse loading or deflection as in the case of bimorph piezoelectric
sensors (Low and Guo 1995; Xu et al. 2009), the dominant stress/strain is that along the
length of the cantilever (direction 1), which is also the major stress responsible for charge
generation. Stresses/strain on the other directions are comparatively smaller which can be ignored without significant errors.
Figure 5.2 shows the cross section of the hair sensor at elevation of z. Assume the length of the hair sensor is L with cross section radius of R; the pair of electrodes is symmetric with the x axis and the positive electrode on the surface of the fiber covers the angle from
–Φ to Φ as shown in Figure 5.2.
Figure 5.2. The cross section of the hair sensor. (The plus and minor signs illustrated the concentrated
charges on the surface of the PZT microfiber (for θ=0) and the black arrows in the circle area illustrated the
generated electric field (for θ=0); The pink arrow indicates the direction of the stimulation and the pink
dotted line indicate the neutral strain plane.)
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According to Eq. 5.2, the generated charge on a small area dA at (r=R, γ) on the upper
electrode is,
dqd=⋅⋅31 εγ ( R , )d A (5.3)
Under small magnitude of bending, the strain in the cross section satisfies the plane
bending assumption. Assuming the direction of the stimulation is θ (Figure 5.2), the strain at point (r=R, γ) on the electrodes can be expressed via mechanics of materials principles as Eq. 5.4.
M⋅λ( R , γ ) MR ⋅− cos( γθ ) εγ(,)R = zz= (5.4) EI EI
In Eq. 5.4, Mz is the bending moment at the section z, λ is the distance to the neutral strain plane
(pink dashed line in Figure 5.2), E is the Young’s modulus of PZT and I is the moment of inertial of the fiber.
For the upper half electrode, the strain induced charge is the integration of Eq. 5.4 from
the angle between –Φ to Φ ,
2 Φ MR⋅−cos(γθ ) d⋅⋅ MR qd= ⋅z (R⋅= dγθ ) 31 z 2sinΦ cos (5.5) ∫−Φ 31 EI EI
The total induced change on the entire positive electrode along the fiber is,
22 LLd⋅⋅ M R 2dR sinΦ cosθ =31 z Φ=θ 31 Q∫∫2sin cos dz Mzzd (5.6) 00EI EI
Similarly, the amount of charges on the negative electrode is the same as shown in Eq.
2 −Φ2dR sin cosθ L 5.6 but with a negative sign, i.e., 31 Mzd . It is evident that the charges EI ∫0 z
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induced on the two electrodes are always same in quantity and opposite in sign. Taking
electrodes as a capacitor, the output voltage can be expressed as Eq. 5.7.
= U QC (5.7)
where C is the capacitance of the sensor, which can be taken as a capacitor formed by the
two opposite arc surfaces and the piezoelectric material in between.
Assuming the electric field is as shown in Figure 5.2, the capacitance can be determined based on the approximation of the parallel plates theory as in Eq. 5.8.
ε ⋅dA Φ εθ⋅⋅LRd CL=r = r =ε Φ (5.8) ∫∫dR ∫−Φ 2 r
In Eq. 5.8, εr is the dielectric constant of piezoelectric material, dA is the area of a differential element and d is the distance between a differential capacitor.
Substitute Equations (10) and (12) to Eq. 5.7, the analytical output voltage is obtained:
2 2dR sin Φ L U= 31 Mzd cosθ (5.9) ∫0 z ε r EIΦ L
From Eq. 5.9, it can be seen that the induced charges on the electrodes are dependent on
the direction of the stimulation (θ), the mechanical property (E) and geometry of the hair
(R, L, I, Φ), the piezoelectric property of the fiber (d31) and the strength of the stimulation
L ( Mzd ). The pattern of variation with loading angle is cos(θ). ∫0 z
5.2.1.2. Numerical fully-coupled modeling
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The performance of the sensor was also evaluated using Finite Element Method (FEM)
with fully-coupled mechano-electrical fields (as described by Eq. 5.1). A multi-physics
modeling software COMSOL® was used due to its advantage to solve coupled physic fields.
The model simulated a piezoelectric hair with a diameter of 250µm and a length of
1000µm, as shown in Figure 5.3a. The piezoelectric properties of commercial PZT were
assigned to the material properties of hair element. Special attention was paid to assign
the piezoelectric coefficient tensor in light of the fact that the fiber is polarized in the d31
mode. The bottom of the hair is assumed to be structurally fixed (all of six degrees of
freedom were fully constrained) and the other faces are set free to deform. Since the
electrode layer is extremely thin (2000Å), and its mechanical influence on the rod is
neglected in the model. The electrodes are modeled as equipotential electrical boundaries
on the surface of the rod. To ensure there is a small gap between the electrodes, the
positive electrode is assumed to cover the area from-5π/12 to 5π/12. One electrode is set as ground and the other set as floating potential boundary. The electric boundaries of all other faces are set as zero charge, which is equivalent to electric isolation condition. The computational domain is fine meshed with 41682 tetrahedral elements to obtain reliable results. Mechanics and electrical modules were coupled to study the sensor transduction behaviors.
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(a) (b)
Figure 5.3. FEM modeling of the proposed sensor design: a) FEM model mesh; b) electrical potential
distribution under point loading acting along y direction (θ=0).
The hair is assumed to be subjected to a point force P of 0.001N on the top of the rod at different directions (Figure 5.3a). Figure 5.3b plots the simulated electrical potential distribution for the loading along the y-direction (θ=0). The two electrodes are equal potential. One of the electrodes is assumed to be grounded, the output voltage by the hair element, therefore, equals to the electric potential on the other electrode. This can be easily obtained from the FEM output data.
The directional sensitivity of the sensor output is studied by changing the direction of the point force while maintaining the magnitude of the point force. The direction of the applied point force varied from 0 to 2π with a step of π/12. For each loading direction, the corresponding sensor output voltage is obtained by the coupled FEM model. Figure
5.4a summarizes the results of sensor voltage outputs. It can be seen that for loading directions of θ=0 and θ=π, the amplitudes of the output voltages are maximum but with opposite polarities. For loading directions of θ=π/2 and θ= 3π/2, the FEM model
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predicted sensor output voltages are close to zero. Directional sensitivity in the cos (θ) is
clearly seen from this plot.
When plotted in the polar coordination system (Figure 5.4(b)), the sensor output with direction of loading appears as a shape close to “8”, which also indicate the variation of the sensor output voltage as a cosine function of the loading direction. Such directional sensitivity is similar as biological hair sensors such as in the neuromasts hair cell of fish.
It should be noted that the applied external stimulations in the analytical and FEM models are both static. However, piezoelectric material is not suitable to measure static stress or strain. Thus the simulations are in the qualitative manner in terms of the exact response amplitude (output voltage); but in terms of the directional sensitivity, both the analytical model (which does not consider the coupling of mechano-electrical fields) and the coupled FEM analyses predict the directional sensitive characteristic of the sensor, i.e., the output voltage from the sensor varies with the direction of load with a cosine function.
The transient response of the sensor is also modeled using the FEM method and the
simulation results are compared to the experimental results. The details of the transient
simulation will be discussed in the following section.
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Figure 5.4. The predicted directional sensitivity of the proposed sensor design. (a) Plot in the Cartesian
coordinate system; (b) Plot in the polar coordinate system
5.2.2. Sensor fabrication and validation of its directional response
A prototype hair sensor using the design concept was fabricated to validate the sensor
design. A PZT microfiber from Smart Material® was used as the transduction element of
the hair sensor. The fiber was 250µm in diameter and 75mm in length. According to
supplier, the material of the fiber was PZT SP53 (or Navy type VI). A thin layer of Ag
(thickness of 2000 Å) was first coated around the surface of the PZT microfiber using the
sputtering technique for the length of around 10mm (Figure 5.5a; Discovery 18 sputtering system, Denton Vacuum LLC). Laser lithography was then utilized to remove the Ag
layer along two lines and create the gaps as shown in Figure 5.5. These treatments result
in a pair of opposite electrodes on the surface of the PZT fiber. The electrodes were then
connected to a pair of wire leads through electrical conductive epoxy (Figure 5.5b).
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Figure 5.5. (a) schematic of sputtering Ag layer on the piezoelectric fiber; (b) the piezoelectric fiber with
electrodes connected to wire leads; (c) the fabricated hair sensor was mounted on an in-house built angle
controller.
The PZT material was then poled with the deposited electrodes by applying a voltage of
1000 volts under the room temperature. This voltage was equivalent to electrical field strength of about 4kV/mm, which was sufficient to permanently align the dipoles in the piezoelectric material, or polarize the fiber.
Although only 10mm section of the piezoelectric fiber is coated with electrode and polarized, the whole length of the piezoelectric fiber was maintained for the subsequent testing. The advantage of keeping a long piezoelectric fiber allowed for applying large loading or deflections as discussed in the following context.
To evaluate the directional sensitivity, the fiber was glue mounted on the ring of an in- house designed angle controller and the gripping zone of the fiber is 5mm (Figure 5.5(c)), resulting a cantilever length of 70mm. By manually adjusting the knob of the controller, the orientation of the ring was adjusted to the resolution of 0.1°. The digital readout precisely displayed the angle of rotation. Since displacements could be controlled more
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accurately and more easily than forces, the hair sensor was stimulated by applying a
prescribed displacement (5 mm from the at-rest position) in the desk plane followed by
an immediate releasing. This stimulation resulted in the free vibration of the hair. The
orientation of the ring was denoted by angle ψ and the direction of the displacement was
denoted as θ, as illustrated in Figure 5.2. The angle ψ was varied from 0 to π with steps of
π/12. At each orientation, the hair tip was displaced in two opposite directions, i.e., θ=0,
π as ψ=0, θ= π/12, 13π/12 as ψ= π/12 … θ= π, 2π as ψ= π. The hair sensor was connected to a computer through a PC oscilloscope (PicoScope® 3206) without any
external signal processing circuits and the signals were sampled with the software
PicoScope 6 (pico®). To eliminate the influence of the AC power, the raw signals are filtered to remove the powerline interference with the cutoff frequency of 60Hz.
Figure 5.6. Laboratory evaluation of the directional responses of the hair sensor. (a) Example signal
responses from different loading directions; (b)The comparison of the FEM simulation and the experiment
result (The prescribed initial displacement is 5mm in the direction of θ=0).
Figure 5.6(a) displays examples of measured free vibrational response by the sensor. A few characteristics of the sensor output signals can be observed: 1) for each loading
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condition, the signal rises to a peak and then damped freely, which is typical of an impulse response; 2) from the signals, the damped natural frequency and the damping ratio can be determined. The damped natural frequency is determined to be about 56Hz and the damping ratio is in the range of 0.1~0.15. It should be noted that the damped natural frequency (56Hz) is consistent with the first natural frequency of the cantilevered fiber calculated using the numerical model, which is 62Hz; 3) for loadings from opposite directions (such as 0° vs. 180°, 45° vs. 225°, etc.), the strengths of sensor signal (highest magnitude of the peaks in the signal) are comparable in the magnitudes whereas the polarities are opposite; 4) from 0° to 90° or from 180° to 270°, the strengths of the signals decrease whereas the polarities of the signals remain the same; 5) at directions of 0° and
180°, the sensor signals shows the highest amplitudes, which indicates they are most sensitive in these directions; while in the orthogonal directions (90° and 270°), the amplitude of the sensor signal are very small, which indicates the sensor is least sensitive in these directions;
The free vibration response of the sensor is also compared to the FEM simulation. In the
FEM model, the fiber is 70mm in length and 250mm in diameter; the fiber is first displaced by a force to ensure that the initial displacement is the same as in the experiments (5mm at the tip); the force lasts for a very short time (5ms) and it is then released. The time step in the force duration is selected as 1ms, and after that the time step is 5ms, a total time of 10s was simulated. Such time steps are chosen to ensure both the numerical stability and accuracy. Figure 5.6(b) shows the response of the fiber after releasing from a prescribed initial tip displacement of 5mm in the direction of θ=0, both from the experiment and the FEM simulation. The signals are normalized by the peak
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voltage. It can be observed that, 1) the experimental result is in a fairly good agreement
with the simulation; 2) the damped frequency of the simulated response is about 60Hz,
which is a slightly larger than that from experiment (56Hz) and fairly close to the first
mode natural frequency of the cantilever fiber (62Hz); 3) the damping ratio of the
experiment signal (0.2) is slightly greater than the simulated one (0.16).
Figure 5.7. Maximum amplitudes of sensor signals under different loading conditions. (a) plot in the
Cartesian coordinate ; and (b) the plot in the polar coordinate
Figure 5.7 plots the maximum amplitude of the sensor signal loaded under different
directions. The plot in the Cartesian coordinate system shows that the magnitude of
sensor outputs follow a cosine variation with the loading direction. The corresponding
plot in the polar coordinate system also appears as an “8” shape. Deviations from a
perfect “8” shape are probably attributed to the imperfection in sensor fabrication or
loading procedures. However, the overall directional sensitivity behaviors of the sensor
are consistent with those of computational modeling analysis (as in Eq. 5.9 and Figure
5.4). This validated that the sensor possesses directional sensitivity as predicted by the
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results of computational model analyses. The behaviors of the directional response resemble that of biological hair cells in fish otolith. Such transduction behaviors pave the technical basis for emulating the unique acoustic tracking strategy by fish.
5.3. PIEZOELECTRIC MICROFIBER BASED HAIR SENSOR WITH SPIRAL ELECTRODES
A disadvantage of the first design is that the fiber itself is fragile. To improve the durability, another design is proposed.
5.3.1. Sensing principle and sensor design
A schematic drawing of the new hair sensor was shown in Figure 5.8(a). It consists of three functional parts: a) the PZT microfiber as the sensor transduction element, b) the spiral wires act as electrodes and provides structural support, and c) an outer shrinkage tube provides confinements and holds the microfiber and spiral wire together. The confining effect from the shrinkage tube and the inner pushing effect from the spiral spring structure ensure good contacts between the PZT fiber and the spiral electrodes.
When the hair structure deflects due to forces or flows, the PZT microfiber deflects together with the whole structure. The surface on which the electrodes are located will stretch or compress correspondingly. Differential deformation on the PZT microfiber between a pair of electrodes results in electrical potential differences due to the piezoelectric effect.
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Figure 5.8. The schematic illustration of the proposed design of the bio-inspired flow sensor and its principle. (a) The electrodes are in spiral shape, “+” and “-” denotes the positive and the negative electrodes,
respectively. The shrinkage tube ensures good contact between the electrodes and the PZT microfiber and holds the structures as a whole; (b) the illustration of the electric field distribution in the PZT microfiber; (c)
the process of electric charges collection can be modeled as the accumulation of the currents in each
element.
This changes the electric field distribution in the PZT microfiber (Figure 5.8(b)).
The actual electric field is non-uniform due to edge and corner effects. However, the
diameter of the PZT fiber is very small compared with the spiral wire. Therefore, it is
reasonable to assume that the electric field between each adjacent pair of electrodes (i.e.,
the pair of contacting points between PZT fiber and spiral wires) is uniform. Such
assumptions are also applied in Paradies and Melnykowycz (2010). The repetitive
sequence of the electrodes pair is similar to the interdigitated electrodes (IDE), which are
widely used in sensor designs (Bent and Hagood 1997, Paradies and Melnykowycz 2010).
The differential potentials on the opposite electrodes will result in accumulation of
electric charges on the surface, and these charges are collected through the Spiral-
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Double-Wire (SDW) electrodes. For convenience, each adjacent pair of electrodes and
the section of PZT microfiber between them are termed as an element in the subsequent
context.
5.3.2. Modeling of the sensing mechanisms
The geometry of the hair sensor structure is very complex to model directly. To simplify the problem, assumptions were made to simplify the transduction structure while capturing the basic sensing mechanisms. Both analytical and numerical models were employed to consider 1) the piezoelectric effect of the PZT microfiber; and 2) the sensing structure made of IDE type electrodes. Due to the repetitive nature of the electrode pairs, one representative element is sufficient to simulate the transduction property of the sensor.
The transduction performance of the entire hair sensor is the combination of all individual sensing elements. For an individual sensing element, the electrodes are assumed as two patches on the surface of the PZT microfiber. Since the spiral spring and the shrinkage tube mainly provides structural support and does not possess a transduction function, it is not modeled. This doesn’t affect the modeling of piezoelectric effects and the directional responses of the whole hair sensor.
5.3.2.1. Qualitative analytical modeling
The analytical model is based on a single element with radius of R and length of L. The geometry and coordinate are shown in Figure 5.9(a). The width and length of the electrodes are a and b, respectively, with center-to-center spacing of s. A point force F is assumed to act in the xoz plane with an angle θ to the z axis. Taking the element as a
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capacitor, the output voltage of the sensor is the net charges (the differential charges
between the opposing electrodes) divided by the capacitance (Eq. 5.6).
Figure 5.9. Analytical model for the transduction mechanism of the proposed hair sensor. (a) An element
with one pair of electrodes subjected to load F; (b) Decomposition of the F normal to the yoz plane and the
corresponding deformation, the inset represents the stress state of the positive electrode (red) area; (c)
Decomposition of the F normal to the xoy plane and the corresponding displaced element, which is a bend
in the xoy plane, the dots inside the electrodes indicate the stress are normal to the xoy plane and towards
the readers under Fz.
QQ+−− U = (5.6) C
where C is the capacitance between the pair of electrodes.
The charges on each electrode can be obtained by integrating the electric displacement or
. charge density at point (x,y) (Dxy) over the whole electrode area A The charge density depends on the piezoelectric property and the stress (Eq. 5.7). It is assumed that only the pure compression and tension contributes to the produced charge and therefore Dxy can
be expressed as Ddxy= 33 ⋅σ xy . d33 is the piezoelectric constant in y direction induced by
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stresses in the same y direction; σxy is the stress at point (x,y). The total charge at the positive electrode is the integration of charge in its contact area with the PZT fiber, i.e.,
= σ QD∫∫xydA= ∫∫ d33 xy dA (5.7) AA++
It is clear that the total charges on the electrode rely on the stress conditions (σxy ) in the areas of
PZT fiber in contact with the electrode. To study the stress conditions, the external force can be decomposed into two orthogonal components: one is normal to the yoz plane (Fx); and the other is
normal to the xoy plane (Fz). Therefore, the condition in Figure 5.9(a) transforms to deformation mode 1 and deformation mode 2 as shown in Figure 5.9(b) and 5.9(c). The stresses on the electrodes for the decomposed conditions can be calculated as (Eq. 5.8).
⋅ Mxxy Fx ⋅−⋅() Lyx FLy⋅−⋅( ) sinθ ⋅ x σ xy = = = (condition 1) II I (5.8) ⋅ Mzxy Fz ⋅−⋅() LyR FLy⋅−⋅( ) cosθ ⋅ R σ = = = (condition 2) xy II I
For deformation mode 1, the distribution of the stress is symmetric with x=0, that is, the
half of the section (x<0) is in compression while the other half (x>0) is in tension. This
symmetry results in zero net charge on the positive electrodes when integrated over the
area of the electrode using equation (Eq. 5.7); similarly, the net charge on the negative electrode is also zero. Therefore, the output voltage for condition 1 is ZERO or mode 1
does not produce electrical output.
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Figure 5.10. FEM model for the performance of the sensor element. (a) The FEM model of the hair element,
which considers only one pair of electrodes along the surface of PZT microfiber; (b) The contour plots of
the electrical potential on the bottom surface of the modeled element (the unit is in Volt and the angle
above each contour plot shows the load direction). In the range of 0-180°, the contours are mirrored with
the 90° condition; (c) The variation of electrical output with loading angle, which shows a figure of “8” in polar coordinate system; (d) Relationship between the predicted sensor output voltage and the magnitude of
applied force (the loading direction is along 0°).
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For deformation mode 2, the neutral plane is at z=0 and both the positive and negative electrodes
are compressed. Substitute (Eq. 5.8) and (Eq. 5.7) to (Eq. 5.6) and use the geometries in Figure
5.9(a), the output voltage can be expressed as (Eq. 5.9).
(Fs⋅) ⋅⋅ R( ab ⋅) Ud= cosθ (5.9) 33 IC⋅
Since deformation mode 1 does not contribute to the output voltage, Eq. 5.9 is the
expression for the overall output voltage of the element responding to point load F. In Eq.
5.9, the term (Fs⋅ ) is the resultant differential moment between the pair of electrodes; the
term (ab⋅ ) is the area of each electrode; I is the moment of inertia of the cross-section,
π ⋅ R4 which is I = for a uniform circular cross-section; C is the capacitance of the 4
capacitor defined by the two electrodes and the PZT material between them. Therefore, C
should depend on the spacing of the two electrodes (s), the radius of the PZT fiber (R)
and the dielectric constant of the PZT material (ε). The analytical expression of C is
difficult to obtain, because it is not only related to the parameters mentioned (s, R and ε), it also depends on the distribution of the electric field (as illustrated in Figure 5.8b). Since the parameters such as I and C are cross design related to s and R, it is hard to evaluate the influence of each parameter (e.g., s and R) on the performance of the sensing element from Eq. 5.9. However, it is confident to argue that the output voltage is linearly dependent on the applied force (F); and it is also dependent on the acting angle (θ) of the external stimulation. It is worth noting that the directional responses of the sensing element follow a cosine function, which is analog to the directional sensitivity found in hair cells in the lateral line system of aquatics.
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5.3.2.2. Numerical Modeling of the Mechano-Electrical Transduction with Finite
Element Method (FEM)
The directional sensitivity of the sensing element was also modeled numerically using
FEM software COMSOL®. The mesh of the FEM model for one sensing element with
two electrodes is shown in Figure 5.10(a). The section of the PZT fiber is assumed to be
250µm in radius and 500 µm in length. The electrodes are assumed to be 100µm in width
and 320µm in length with center-to-center spacing of 300µm. The piezoelectric and the
mechanical properties of the PZT fiber are based on the datasheet of product No. 5H2 by
Smart Material Corp.. The whole structure is meshed into 13629 tetrahedral elements and
the stationary solver is used to solve the fully coupled piezoelectric problem. For the
mechanical part, the bottom of the element is under fixed constraints while the other
boundaries are free to deform; a horizontal load is applied to the top surface of the
element along different directions. For the electrical part, the lower electrode is set as
ground and the upper electrode is set as floating potential boundary and all the other
boundaries are set as zero charges. Such boundary settings guarantee that the electric
potential of the upper electrode is the output voltage of the sensor. To study the
directional responses of the sensing element, a horizontal surface force of 100N/m2 is applied and the direction of the load is swept from 0° to 360° with steps of 15° (the
convention to define the angle is shown in Figure 5.10(a) and it is the same as in Figure
5.9(a)). To study its response under variable forces in the same direction, the force
changes from 0 to 500N/m2 with steps of 20N/m2 at the direction of 0°.
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To illustrate the piezoelectric effect, Figure 5.10(b) shows the change of the electrical
potential distribution on the bottom surface of the element under force of 100N/m2 at each direction from 0° to 180°. It shows that the distribution of produced electrical potential is symmetric with the loading direction in terms of amplitude, but opposite in polarity. Along the loading direction of 90° and 270° the electrical potential is almost zero. Regarding the zero line as “equator”, the maximum and minimum values located at the “poles” of the circle. It can also be concluded that the distributions for all the steps are mirrored with the 90° step. For example, responses to load applied at 0° angle (with x- axis) is mirrored with that at 180°, responses to load at 15° is mirrored with that at 165°, etc.
To quantitatively illustrate the performance of the sensor, the directional sensitivity and linearity of the sensor output was analyzed by FEM simulation. The simulated output voltage of the sensor, i.e., the electric potential on the upper electrode, is used as the performance criterion. Two different cases are analyzed. The directional sensitivity is summarized for a constant horizontal force of 100N/m2 acting along different loading
directions. The sensor outputs versus loading directions are plotted in Figure 5.10(c) in a
polar coordinate system. The curve shows a clear “8” shape, which indicates that the
output voltage of the sensor follows a cosine function of the loading direction. The linearity of the sensor is summarized for varying magnitudes of forces in the same direction of 0°. The summary of sensor outputs versus magnitude of the loads is shown in
Figure 5.10(d), which follows a linear relationship. These results are consistent with the conclusions drawn from the simplified analytical model (Eq. 5.9).
5.3.3. Prototype fabrication and evaluation
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5.3.3.1. Fabrication in the macro scale
To validate the sensing concept, a sensor prototype was fabricated first in the macro scale.
A pair of bare conductive wires separated with two rubber wires was first carefully twined along a copper rod to form the spiral electrodes. The spacing between the bare conductive wires was checked under a microscope to ensure the spacing between wires were uniform. A piezoelectric microfiber (Smart Material Corp.) with a diameter of
250 µm was inserted to a well fitted metal tube, whose inner diameter was slightly larger than the diameter of the fiber. The metal tube with the microfiber was placed to the side of the spiral wires and these two parts were then confined with a shrinkage tube. After this, the metal tube was pulled out slowly with great care to leave the microfiber in place.
Excellent contact between the microfiber and the SDW was guaranteed by the contraction force from the outer shrinkage tube. The two separation rubber wires and the copper rod
were then taken out sequentially. The hair structure was then welded to a base pad and
the wire was connected with the electronic lead. The final hair structure is shown in
Figure 5.11.
Figure 5.11. A fabricated biomimetic “hair” sensor in macro scale. The “hair” is 1 mm in diameter and 40
mm in length.
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We called the spring-like structure formed by the two bare conductive wires the Spiral-
Double-Wire. It not only serves as the spiral electrodes to collect the charge produced by the piezoelectric fiber, but also provides the structural support and has a major effect on the dynamic responses of the hair sensor. To ensure strong sensor signal outputs, the piezoelectric microfiber was polarized under a voltage of 2K volts through the SDW electrodes.
5.3.3.2. Laboratory evaluation of the artificial hair sensor
The performance of the fabricated sensor was evaluated with a laboratory set up illustrated in Figure 5.12(a). The base pad of the sensor was attached to a platform which can be controlled by a precise angle controller. The output of the “hair” sensor is directly connected to a PC oscilloscope (OSC) (PicoScope® 3206) without any signal amplification. The signals were filtered through the software PicoScope 6 (Pico
Technology®) using a low-pass filter with cutout frequency of 60Hz to eliminate the influence of the AC power interference.
To study the sensor responses, the tip of the hair sensor was displaced with a prescribed distance. It was then released to produce free vibrations, as shown in Figure 5.12(b). The vibrations produced charges in the PZT microfiber, which were collected by the SDW electrodes. The response of the hair structure, which was an impulse response, was recorded and displayed using the PC OSC. The sensitivity and directional responses of the hair sensor were studied in controlled experiments where the direction and amplitude of deflection at the tip of the hair sensor were accurately controlled.
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Figure 5.12. Laboratory setup for the characterization of the hair sensor. (a) The “hair” was attached to a
customer designed accurate angle controller; (b) Illustration of the loading process. The tip of the “hair”
was first displaced to a prescribed distance away from its rest position and then suddenly released to make
it to vibrate freely.
a) Directional responses of hair sensor
Figure 5.13. Sampled signals of the sensor under different loading conditions.
The direction is defined as the angle from the direction of the tip displacement to the z
axis in Figure 5.9 and is changed from 0° to 360° by steps of 15° by the angle controller.
At each direction, sensor responses to three different displacement magnitudes, i.e., 5mm,
10mm and 15mm from the resting position were measured. The testing was repeated seven times at each loading condition to ensure the responses were consistent. To
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illustrate the direction-dependent signal responses, a few representative signals are
plotted in Figure 5.13. A few observations can be made from Figure 5.13. a) for a given
direction (i.e. 0° or 180°), the sensor output signal increases with the deflection magnitude of the hair tip; b) for opposite directions, i.e. 0° and 180°, the signal amplitudes are comparable while the polarities are opposite; c) for direction angle of 90° and 270°, sensor output is negligible; d) the free vibrations of the hair sensor correspond to a natural frequency of around 18Hz. To qualitatively evaluate the dependences of the
signal on the loading directions and amplitudes, we define the first peak voltage of an
output signal as the output voltage. With a prescribed tip displacement of 15mm, the
averaged output voltages for each loading direction are plotted in Figure 5.14(a), which
shows a clear figure of “eight”. The result indicates that the sensor signal output follows a
cosine function with the loading direction, which is in agreement with the qualitative
analytical modeling (4) and the quantitative numerical modeling (Figure 5.10(b)).
Figure 5.14. Results of measured sensor signals. (a) Directional sensitivity: the output voltage is dependent
upon the loading directions and shows an “8” shape. (b) relationship between the output voltage of the hair
sensor and its tip deflection.
b) Linearity of the sensor
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For a given loading direction, the sensor output voltage is dependent on the amplitudes of
the prescribed displacements. The output voltages for hair sensor deflections of 1mm,
3mm, 5mm, 10mm and 15mm at different directions of 0°, 90°, 180° and 270° are plotted
in Figure 5.14(b). Overall, there is a good linear relationship between the output voltage
and the hair sensor deflection. There, however, appears to be a threshold for sensor
linearity which is roughly 3mm (Figure 5.14(b)).
c) Implication of directional responses of the hair sensor
From the experimental results, the sensor output voltage U can be described as a function of direction θ and amplitude x of the sensor tip deflection shown in Eq. 5.10.
Ux( ,θθ )= Ux,0θ = ⋅ cos =Ax( −⋅ x0) cos θ ( x > x0) (5.10)
Figure 5.15. (a) the measured response signals from two hair sensors aligned with different spacing
subjected to burst-induced air flows (the hair sensor in the upstream of the burst is noted as “US” and the
one in downstream as “DS”); (b) the relationship between the spacing of the two hair sensors and
corresponding measured time delays.
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One should note that Eq. 5.10 is different from Eq. 5.9 in that Eq. 5.10 has an extra term
x0, which is the tip displacement threshold of the sensor. In Eq. 5.10, U x,0θ = is the output
voltage of the sensor in the direction of θ=0, which is a linear function of the initial tip
displacement x (Figure 14b). A is a constant and both of A and x0 can be determined from
the experimental data (e.g. Figure 14b). Since the relationship between the output voltage
and the prescribed displacement is analogy to that between the output voltage and load F,
the following equation is also true (Eq.5.11), in which F0 is the force threshold of the
sensor.
UF(,)θθ= AF( −⋅ F00) cos (FF >) (5.11)
Given two sensors with the same sensitivity arranged in different directions and placed very close to each other so that they are assumed to experience the same external load, the external load can be determined using the signals from the pair of sensors (Eq. 5.12), where θ1 and θ2 are the directions of the load corresponding to the two sensors.
U(,) Fθθ = AF( −⋅ F) cos 1 01 (5.12) U2(,) Fθθ= AF( −⋅ F02) cos
For a particular case where the two sensors whose most sensitive directions are orthogonal to
π each other, or θθ= − , the amplitude and direction of the load can be expressed as (Eq. 5.13), 212 where θ1 is the direction of the load corresponding to one of the sensors.
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UU22+ FF=12 + A 0 (5.13) U θ = arctan 1 1 U 2
If the load is induced by flow instead of a point load, similar algorithm can be used to determine the flow velocity with a similar pair of sensors.
5.3.4. Application of the proposed sensor as a flow sensor inspired by the lateral line
It has been found that fish use a spatially coded array of neuromasts to retrieve flow
information. It was recently found that the lateral line is a turbulence sensor in that it senses flow not due to the steady component, but due to the turbulence component
(Chagnaud et al 2008a). By measuring the signals from pairs of neuromasts in the lateral line of goldfish, researchers found it is possible for fish to estimate the flow speed by sensing the time delay as flow turbulence passes different neuromasts.
To emulate the flow sensing mechanism of fish, two hair sensors were aligned in tandem in the same direction and were exposed to air bursts produced by a calibrated syringe.
The syringe was well-controlled to introduce air burst with velocity of 16m/s, 12m/s,
8.5m/s and 5.5m/s. The burst traveled to the two sensors and cause them to vibrate. The distances of the two hair sensors were varied from 50mm to 200mm with steps of 50mm.
Examples of measured signals from the two sensors with different spacing are illustrated in Figure 5.15(a). A time delay is observed between the two sensor responses and the time delay increases with the spacing of the pair of sensors. Similar as the lateral line system (Chagnaud et al 2008a,b), the velocity of burst propagation can be calculated by
λ dividing the distance (λ) by the time delay (Δt), i.e., V = . ∆t
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The time delays determined from analyzing the time responses are plotted versus the spacing between the two hair sensors (Figure 5.15b). From Figure 5.15b, it can be concluded that the time delays increase linearly with hair sensor spacing. The calculated velocity of air burst is 15.45m/s, 11.65m/s, 8.5m/s, and 5.5m/s, respectively. It is concluded in that the error of calculated velocities fell within 1.5%~3.5% of the controlled burst velocities, which was monitored by a hot wire thermo-anemometer from
EXTECH®, Model 407123. This conceptual experiment proved that the proposed hair sensor has the potential to emulate the fish neuromasts to sense flow speed.
5.4. PIEZOELECTRIC MICROFIBER BASED HAIR SENSOR WITH ARTIFICIAL CUPULA
5.4.1. Inspiration and sensor design
Compared to the first design (with surface electrodes), the second design (with spiral electrodes) provides much better durability. A main drawback of the second design, however, is that the fabrication process is complex and it relies much on manual manipulation. An ideal design might be the one which is durable as well as easy to fabricate.
Further inspired by the structure of the fish superficial neuromast, in which the hair cells are encapsulated with complaint cupula, the durability of the piezoelectric hair sensor with surface electrodes) is improved by embedding the piezoelectric microfiber in a host material (Figure 5.16). The structure of the superficial neuromast of fish inspires the design of the “composite sensor”, that is, the sensing element (piezoceramic material) is embedded in another host material which is more compliant (artificial cupula). The cross- section of the composite sensor is shown in Figure 5.16b.
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(a) (b)
Figure 5.16. The design of the hair sensor with artificial cupula. (a) The composite design; (b) The cross-
section of the improved design with the artificial cupula. R, r, and s is the diameter of the host cylinder, the
diameter of the microfiber, and the distance between the center of microfiber and the host material,
respectively.
To achieve best performance of the sensor, two questions should be answered first: 1) what’s the optimal geometry of the sensor? 2) what type of material should be selected for the host material? An in-depth analysis of the response of the sensor is required to answer the questions.
In this Section, the governing parameters and their influences on the performance of the sensor are studied with a simplified analytical model; the sensitivity of the sensor is also modeled numerically with a fully-coupled model with the assistance of computer
simulation, considering the complex geometry of the composite sensor, the unique
pattern of the electrodes, and the mechano-electrical coupling process.
5.4.2. Modeling and optimization
The original hair sensor is designed to have directivity similar to the hair cells in fish (Eq.
5.14).
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UU(θθ) =θ =0 ⋅cos (5.14)
The sensitivity of the sensor (S) is defined as the ratio between the output voltage at the
Uθ =0 zero degree direction (Uθ=0) and the applied force (F): S = . F
5.4.2.1. Analytical pure mechanical model
To qualitatively identify the governing parameters affecting Uθ=0, the ideal pure mechanical model is first employed, assuming Uθ is linearly proportional to the average strain in the piezoelectric fiber. This assumption is further validated using the more accurate (fully coupled) Finite Element Method (FEM) in the following section.
A constant force (F) is applied on the top of the composite sensor at the direction of θ=0, which is defined following the angle convention as illustrated in Figure 5.16b. To determine the location of the neutral axis when the sensor is bended, the composite sensor can be treated as the combination of three independent components (Figure 5.17).
These three components are: 1) a “positive” complete cylinder with diameter R, of the host material; 2) a “negative” cylinder with diameter r, of the host material, at the location of y=s, x=0; and 3) a “positive” cylinder with diameter r, of the piezoelectric material, at the location of y=s, x=0. The neutral axis is assumed located at y=y’, with the reference y=0 as shown in Figure 5.18. The modulus of the host material is assumed to be smaller than that of the piezoelectric fiber; therefore the neutral axis is located in the lower half of the sensor (Figure 5.18).
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Figure 5.17. Equivalent components of the composite sensor
Assuming that the structure is in pure bending, the location of the neutral axis can be determined as Eq. 5.15. In Eq. 5.15, Eh and Ep is the elastic modulus of the host material and the piezoelectric fiber, respectively; Ah and Ap is the cross-section area of the complete host cylinder and the piezoelectric fiber, respectively; y’, yh, yp is the location of the neutral axis, the location of the centroids of the complete host cylinder and the piezoelectric fiber, respectively.
EAy−+ EAy EAy y ' = hhh hpp ppp (5.15) EAhh−+ EA hp EA p p
Rs E Set =n, = µ , and p =η , the location of the neutral axis of the composite sensor can rr Eh be non-dimensionalized as shown in Eq. 5.16.
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(a)
(b) (c)
Figure 5.18. Sensitivity of the sensor: a) with different n, η and μ; b) with different η and μ, while n=4 c)
with different n and μ, while η=60.
n3 +−(ηµ1) yr' = ⋅ (5.16) n2 +−(η 1)
The average strain at the centroid line of the piezoelectric fiber is the integration of the strain at the fiber’s centroid along the whole length of the sensor (Eq. 5.17). In Eq. 5.17,
L is the length of the sensor, EI is the equivalent stiffness of the composite sensor, which can be calculated using Eq. 5.18 or its dimensionless form, Eq. 5.19.
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L FLz⋅−( ) ⋅−( yy') d z ∫0 EI ε = ys= (5.17) centroid L
2 22 EIEI= +− Rz''πππ R22 − EI +− zs r + EI +− zs ' r 2 hh( ) hp( ) p p( ) (5.18)
2 π r 4 (n − µ ) = ⋅42 +ηη −+ − EI Eh n14 n ( 1) 2 (5.19) 4 n +−(η 1)
Substitute Eq. 5.19 to Eq. 5.17, the average strain on the centroid line of the piezoelectric fiber is:
2 2FL⋅ ηµ⋅−nn( ) ε = ⋅ (5.20) centroid Erπ 3242 2 p (n+−η1)( n +−+ η 14) nn( ηµ − 1)( −)
Eq. 5. 20 clearly indicates that the average strain on the centroid line of the piezoelectric fiber is linearly depends on the applied load (F) and the length of the sensor (L). The second term in Eq. 5. 20 is considered as the centroid strain coefficient, which describes the influence of configurations of the composite sensor on the bending of the sensor. The parameters include the diameters of the host material (n) and the piezoelectric fiber (r), the stiffness of the host material (η) and the eccentricity of the piezoelectric material (n-
μ)r. The centroid strain coefficient is plotted in Figure 5.18, from which the influence of each parameter (n, η, μ) can be evaluated.
With increasing relative eccentricity (μ) of the piezoelectric fiber, the coefficient also increases for the same diameter ratio n and modulus ratio η; given a certain eccentricity, the coefficient surface defined by both n and η is hump-shaped (Figure 5.18a); the coefficient with same n values and increasing η values follows an increasing-then- decreasing fashion and the optimal η values to achieve the highest coefficient become
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slightly larger for increasing μ values (Figure 5.18b); the coefficient with same η values and increasing n values also follows an increasing-then-decreasing fashion and the optimal n values to achieve the highest coefficient become larger for increasing μ values
(Figure 5.18c). Overall, the changing of the centroid strain coefficient with the governing parameters is not only nonlinear, but also non-monotonic.
Therefore, the sensitivity of the sensor is determined by both the geometry and mechanical properties of the sensor components. To achieve certain sensitivity, there are different combinations of geometries and mechanical properties. For example, if the geometry of the sensor is fixed due to the fabrication limits, the optimal host material to achieve highest sensitivity can be determined by calculating its elastic modulus;, an easy
∂ε method to obtain the optimal value for η is by setting centroid = 0 (e.g, η =117.26 when ∂η opt
n=5 and μ=1.5). On the other hand, if the available materials are limited, one can
determine the geometry of the composite sensor to achieve certain sensitivity.
5.4.2.1. Numerical models: pure mechanical and coupled mechano-electrical model
In the analytical model in the previous section, only one loading condition is studied, that
is, a constant load in the direction of θ=0. The linearity of the sensor in this direction can
be explained with Eq. 5. 20. However, the analytical expression for the elastic strain in
other directions is not derived in this work due to the non-symmetry nature of the sensor,
which results in different equivalent stiffness and different neutral surfaces with external
load with different directions. Therefore, the linearity and the directionality of the sensor
are not validated directly. Furthermore, the output voltage of the sensor is assumed to be
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linearly proportional to the average strain on the centroid line of the PZT fiber. And this
assumption needs further validation.
In this section, the fully coupled piezoelectric model is employed to study the both the
mechanical and the electrical response of the sensor. The governing equations for the
fully coupled model are shown in Eq. 5. 21. In Eq. 5. 21, S and T is the mechanical strain
and stress, respectively; D and E is the electric displacement and electric field,
respectively; sE is the elastic compliance tensor in condition of constant electric field and
εT is the dielectric permittivity in condition of constant stress status; and d is the
piezoelectric coefficient.
S= sE T + dE T (5.21) D=ε E + dT
The fully coupled equations (Eq. 5. 21) are solved using Finite Element Method (FEM) in
COMSOL®. The geometry of the sensor is fixed in the FEM models to focus on the influence of external loads and the modulus of the host material on the performance of the sensor. The diameter of the PZT fiber is 10μm, the diameter of the host cylinder is 50
μm, and the length of the composite sensor is 1mm. These parameters are chosen to mimic the length scale of the neuromasts in fish. The typical length of the superficial
neuromasts is in the range of 40 to 300μm (Blaxter and Fuiman, 1989), depending on the
position on the fish body. One end of the sensor is fixed and the other end is subjected to
a constant force.
The electrical boundary condition of the inner-side and outer-side electrode is floating potential and ground, respectively (Figure 5.19). Therefore the electric potential of the
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outer-side electrode is kept as zero and the electric potential of the other electrode is
determined by calculating the potential difference between the two electrodes based on
Eq. 5. 21.
Figure 5.19. The meshed domains and the electrical boundary conditions
The material of the piezoelectric fiber is PZT 5H and the modulus of the host material is
-2 4 defined by EEhp=η ⋅ , and η changes from 10 to 10 . The domains are meshed with
tetrahedral elements (total number: 7.9×105); the mesh size of the PZT domain is fine
enough to make sure that there are at least three layers of elements in the “gap” region between the two electrodes (Figure 5.19) and this treatment is to ensure the resolution in
this region.
(a) (b) Figure 5.20. The linearity (a) and the directional sensitivity (b) of the sensor
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The linearity of the sensor in a particular loading direction is validated (Figure 5.20a).
The average centroid strain in the PZT fiber increases linearly with the external force (in
Figure 5.20a, the load is in the direction of θ=0); furthermore, the output voltage of the
sensor is indeed linearly dependent on the average centroid strain. These linear
relationships validated the assumption made previously. The directivity of the sensor is
studied by altering the loading directions (Figure 5.20b). It is validated that with the PZT
fiber embedded in the host material eccentrically, the output voltage of sensor still
depends on the loading direction with a cosine function, which is the same with the
directivity of the bare PZT fiber sensor (Section 5.2) and hair cells in neuromasts
(Coombs, 2001).
The neutral axis locations in the composite sensor with different host materials (i.e.,
different Eh or η values) are determined using the FEM model; and the results are compared with those calculated using the analytical pure mechanical model (Eq. 5.16); an additional FEM based pure mechanical model is also built to validate the analytical model. The neutral axis locations determined by these three approaches are plotted in
Figure 5.21a.
Figure 5.21a shows that the neutral axis locations with different η values predicted by three methods are consistent to each other very well; it validated the efficiency of the simplified analytical model, which is more convenient to study the influence of each parameter on the performance of the sensor (Figure 5.18). As η increases, the neutral axis moves towards the centroid of the fiber. For example, two representative locations are illustrated in Figure 5.27a: when η is extremely large or the stiffness of the sensor is mainly determined by the PZT fiber, the neutral axis is approximately located at A (i.e.,
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the centroid line of the PZT fiber); when η is 1 or Ep and Eh is equivalent, the neutral axis is located at C (i.e., the centroid line of the composite sensor).
(a) (b)
Figure 5.21. (a) The calculated neutral axis locations (a) and average strain on the centroid axis (b) for
different host materials with different models
It can also be observed that although very small, there is a discrepancy between the FEM
based pure mechanical model and the fully coupled model. For example, the predicted
neutral axis locations by the fully coupled model are slightly lower than those predicted
by the pure mechanical model. This is caused by the coupling between the mechanical
field and the electrical field (Eq. 5. 21). The deformation induced electric field tends to
“oppose” such deformation and thus makes the PZT fiber slightly “stiffer”. Therefore, the neutral axis locations based on the coupled model are slightly closer to the PZT fiber.
Figure 5.21b shows the calculated average strain on the centroid line of the PZT fiber.
From Figure 5.27b, the optimal value of η determined by the coupled model for the highest sensitivity is 117, which is almost identical to that predicted using Eq. 5. 20. In practice, the material with modulus of the exact optimal value may not exist; therefore we
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define an acceptable modulus range, which covers all the η values between 95% ηopt and
100% ηopt. This range can be determined from Figure 5.27b, which is 46~300. It can be
also observed that the calculated strain based on the coupled model is slightly lower than
that predicted based on the pure mechanical FEM model. This is another evidence for the
fact that the apparent stiffness of the PZT fiber is stiffer when the piezoelectric effect is considered. Compared with Figure 5.21a, another interesting observation is that when the sensor achieves the highest sensitivity, the neutral axis is lower than B, which is the intersection line of the AC plane and the surface of the PZT fiber. That is to say, it is
“inside” the PZT fiber, or, the entire PZT fiber is not in a pure tension or pure compression state.
The results in this section underscore the importance of the matching between the piezoelectric material and the host material (artificial cupula) in terms of both geometry and mechanical property. Since this is only related to the mechanical-mechanical process, this requirement to achieve optimal sensitivity is termed as “mechanical matching”. To determine the optimal design parameters (n, μ, η), the simplified mechanical model (Eq. 5.
20) is recommended due to its simplicity and relatively high accuracy; to determine the sensitivity of the sensor more accurately, the fully coupled FEM model is recommended since it accounts for the piezoelectric effect.
5.5. INFLUENCE OF SHUNT-DAMPING CIRCUIT ON THE DYNAMIC RESPONSE OF THE BIO-
INSPIRED SENSOR
The dynamic response of the sensor is critical for flow sensing applications. Traditional
methods to modify a sensor’s frequency response (e.g., attaching a mass to the sensor or
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altering the geometry of the sensor) are challenging to apply in the micro-scale. An innovative approach is explored inspired by the shunt circuit damper, usually seen in the damping control of structures. By connecting the piezoelectric sensor to an external circuit, part of energy generated due to the vibration of the sensor would dissipate through the shunt circuit. This method is often used to increase the damping of vibrating structures. The influence of shunt-damping circuit on the dynamic response of the novel hair sensor is evaluated in this study. This work aims to study the frequency response of this composite sensor using numerical modeling method, which is capable to model the fully coupled mechano-electrical-circuit system.
5.5.1. Theoretical basis and implementation in COMSOL®
5.5.1.1. Theoretic Basis
To illustrate the theoretical basis in this study, the system shown in Figure 5.22 is used.
The sensor is assumed to connect to an external circuit consisting of a resistor R and an inductor L in parallel.
This system can be termed as a mechano-electrical-circuit system, which involves coupling among mechanical and electrical fields in the sensor and with the external circuit. The governing equations describing the dynamics of the electro-mechanical system connected to an external circuit is well defined and Eq. 5.22 is the modal model of the sensor, derived based on the equilibrium of force and electrical charge in the system.
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kk2 ⋅+ ⋅+ +me ⋅+ me ⋅= mz dz kmm z q 0 CCpp (5.22) L q Lkme k me Lq+ q + + ⋅+z ⋅= z 0 CRp C pp CR C p
in which m, d and z are the modal mass, the modal damping coefficient and the modal displacement, respectively; kmm and kme is the modal stiffness contributed by the
mechanical field and the electrical field, respectively; V is the voltage between the two
electrodes; q is the electric charge on the electrodes and Cp is the inherent capacity of the
piezoelectric fiber; the derivatives are with respect to time t.
Figure 5.22. The hair sensor connected to a shunt circuit.
The piezoelectric effect can be described using the fully coupled electrical-mechanical model (Eq. 5.21). To study the effect of the external circuit on the frequency response of the sensor, this model need to be future coupled with the external circuit.
The deflection z and the charges q on electrodes in Eq. 5.22 are the integration forms of the strain S and electric displacement D in Eq. 5.21, respectively. Therefore, Eq. 5.22 and Eq. 5.21 set the theory base of the coupled circuit-electrical-mechanical model.
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5.5.1.2. Implementation in COMSOL®
As for implementation in COMSOL®, the circuit elements are modeled with general purpose circuit simulator SPICE (Simulation Program with Integrated Circuit Emphasis) and are coupled with the piezoelectric model through the electrical boundary conditions of the sensor. The ODEs in the SPICE for the external circuit are based on the Ohm’s law.
For the RL parallel circuit as shown in Figure 5.22, the ODEs for the external circuit read,
III=+==12;; URIULI 1 2 and I =− q (5.23)
The electric boundary conditions of the inner-side and outer-side electrodes on the piezoelectric microfiber are all set as floating potentials, but with the charges on the electrodes specified as qtop and qbottom, respectively (Figure 5.22). These two parameters
are also used in the SPICE to calculate the current (Eq. 5.23) and in this way, the electrical-mechanic model and the circuit model are coupled.
The diameter of the PZT fiber is 10μm, the diameter of the host cylinder is 50 μm, and the
length of the composite sensor is 1mm. These parameters are chosen to mimic the length
scale of the neuromasts in fish. The host material is polyethylene, which is commonly
used in MEMS design. One end of the sensor is fixed and the other end is subjected to a
contact force. The external load is a harmonic point force (F=0.01N) in the z direction
with angular frequency of ω, acting on the free end of the sensor.
The domains are meshed with tetrahedral elements (total number: 7.9×105); the mesh size
of the PZT domain is fine enough to make sure that there are at least three layers of
elements in the “gap” region between the two electrodes and this treatment is to ensure
the resolution in this region.
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5.5.2. The influence of the external circuit on the frequency response of the sensor
Figure 5.23. Four configurations of the shunt circuit is studied
The frequency response of the sensor is studied by sweeping the angular frequency of the
external harmonic force around the first mode eigenfrequency. Two extreme conditions,
the open circuit and short circuit are also studied to provide a comparison base.
The typical procedure is as following, 1) the first mode eigenfrequencies (fopen and fshort)
for open circuit and short circuit conditions are first calculated using COMSOL®; 2) the
frequency step (fstep) for sweeping is determined as (fopen- fshort)/2; sometimes, the step
size is further refined around (fopen- fshort)/2; 3) the sweeping range is determined as (fopen-
fshort)/2 ±10× fstep.
The inherent mechanical damping of the sensor is considered to constrain the maximum amplitudes of the spectral resonance peaks. Rayleigh damping is assumed, which typically includes mass damping and stiffness damping (Eq. 5.24).
CMK=αβ + (5.24)
In Eq. 5.24, C, M and K is the damping matrix, mass matrix and stiffness matrix, respectively. α and β is the mass damping parameter and stiffness damping
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parameter, respectively. The value of the parameters can be determined experimentally through the time domain response of the sensor. In this study, the stiffness damping parameter is 5×10-8s.
The effect of the external circuit components is studied by sweeping each circuit parameter (i.e., resistance and inductance). Four external circuit types are studied: R only,
L only, RL in parallel, and RL in series (Figure 5.23).
5.5.2.1. Resistor Only
When the external circuit consists only a resistor (Figure 5.23a), the ODEs for the external circuit read,
U= RI; I = − q (5.25)
The effect of the resistance on the frequency response of the sensor is studied by changing the resistance from 103ohm to 107ohm. The absolute value of the displacement of the sensor tip in the z direction is plotted as the spectrum response curve (Figure 5.24a)
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(a)
(b)
Figure 5.24. Sensor with an R only circuit: The spectrum response curve (a) and the effect of the
resistance on the peak value (b).
From Figure 5.25, it can be observed that, 1) when the resistance is very large (e.g.,
107ohm), the sensor response is similar to the condition of open circuit; on the other hand, when the resistance is very small (e.g., 103ohm), the sensor response is similar to the condition of short circuit; 2) when the resistor has interim resistance, the peak value of
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the tip displacement is smaller, compared to those in the condition of open/short circuit; with increasing resistance, the peak value first decrease, then increase (Figure 5.24b); the peak value reaches its minimum when the resistance is 105ohm; and the reduction of the peak value is up to 47%.; 3) with increasing resistance, the eigenfrequency gradually shift from fshort to fopen.
5.5.2.2. Inductor Only
(a)
(b)
Figure 5.25. Sensor with an L only circuit: The spectrum response curve.
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When the external circuit only consists of an inductor (Figure 5.23b), the ODEs for the external circuit read,
U= LI; I = − q (5.26)
Changing the inductance from 0.01H to 10H, its effect on the frequency response of the sensor is evaluated (Figure 5.25). Similar to the resistor only circuit, when the inductance is very small (e.g., 0.01H), the sensor response is similar to that for short circuit; when the inductance is very large, on the other hand, the sensor response is similar to that for open circuit. With a medium inductance, the response of the sensor changed significantly
(e.g., L=1H, Figure 5.25b). There are two peaks in the spectrum response curve, and the peak values (0.017mm and 0.004mm) are much smaller compared to the open/short condition (0.051mm). Different from the pure resistor case, the eigenfrequency of the system is not in the range of fshort to fopen.
5.5.2.3. RL in Parallel
When the external circuit consists of a resistor and an inductor in parallel, the ODEs for the circuit are described in Eq. 5.23. The resistance is kept as constant and the value of
105ohm is assumed. The inductance is changed from 0.1H to 20H and the spectrum response curve is shown in Figure 5.26a.
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(a)
(b)
Figure 5.26. Sensor with a parallel RL circuit: The spectrum response curve (a) and the effect of the
inductance on the peak value (b).
It can be observed that, 1) If the inductance is very small, the response of the sensor is similar to the case of short circuit; 2) with the inductance increasing, the peak value of the tip displacement first decreases dramatically and then increases gradually and finally tends to reach a stable state; The peak value for this stable state is similar to the peak value for the case where the external circuit only consists of a resistor with R=105ohm; 3)
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the eigenfrequency increases gradually from fshort and tends to stabilize at a frequency
slightly smaller than that for the case where the external circuit only consists of a resistor
with R=105ohm.
5.5.2.4. RL in Series
For an external circuit consists of a resistor and an inductor in series (Figure 5.23d), the
ODEs for the circuit read,
U=+=− RI LI; I q (5.27)
The resistance is also kept as a constant, i.e., 105ohm, and the inductance is changed from
0.01H to 10H. From the spectrum response curve (Figure 5.27a) and the comparison of
peak tip displacements for different inductance values (Figure 5.27b), it can be observed
that, 1) with a very small inductance (i.e., 0.01H), the effect of the inductor is negligible
and the sensor response is similar to the case without a inductor; 2) when the inductance
is very large, the external circuit reduced to an open circuit; 3) the peak value reaches its minimum when the inductance is 1H and the minimum peak value is smaller than that for the parallel RL circuit; 4) with increasing inductance, the eigenfrequency first increase
gradually and can be larger than fopen; but with very large inductance, the external circuit
is equivalent to an open circuit and the eigenfrequency will also reduce to fopen.
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(a)
(b)
Figure 5.27. Sensor with a parallel RL circuit: The spectrum response curve (a) and the effect of the
inductance on the peak value (b).
5.5.2. Comparisons and discussions
To further identify the effect of each circuit component (resistor, inductor) on the frequency response of the sensor, comparisons between different circuit configurations are made in terms of peak value reduction, and frequency shift.
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From Figures 5.24-5.27, it can be concluded that when the sensor is connected to an
external circuit, the peak amplitude of the sensor displacement will either decrease or not
change. This reduction of the peak value can also be termed as damping. There are only
two cases when the peak amplitue does not change when the sensor is connected to a
external circuit: 1) the circuit is equivalent to a short circuit; 2) the circuit is equivalent to
a open circuit. Except such cases, the peak value will always reduce, due to the existence of the external circuit. In other words, the damping of the sensor is enhanced.
An “optimal” value for the resistance or inductance exist to achieve largest peak value
reduction. From the limited data obtained from this study, it can be concluded that, the
optimal resistance and inductance only depends on the sensor itself, it does not depend on
the configeration of the external circuit, whether they are connected in parallel or in
series. However, the circuit configeration indeed affects the peak value reduction even
when other factors are all the same. Figure 5.28 provides a direct comparison of the
spectrum response curve for different external circuit configerations.
Figure 5.28. Comparison of the spectrum response curves
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Figure 5.28 indicates that all these three circuits (R only, RL in parallel, RL in series) will increase the damping of the sensor. When a resistor is connected to the piezoelectric
sensor, a part of the electric energy will be consumed/dissipated by the resistor. Therefore
the damping is enhanced. The addition of the inductor will further enhance the dissipation
of the energy and thus further reduce the peak amplitude. The reduction is 47%, 57% and
72% for the R only circuit, the parallel RL circuit and the series RL circuit, respectively.
The explanation of the differences between the parallel and series RL circuits requires
more sophisticated analysis on the coupled equation systems of the mechano-electrical-
circuit model. From the limited data in this study, however, a hypothesis is that with
different circuit configurations, the superposition of the effect of resistor and inductor is
different. For an inductor only circuit, the optimal inductance results in a spectrum curve
with dual peaks, as shown in Figure 5.25b. The effect of an RL circuits can be
considered as the superposition of effect of an R only circuit and an L only circuit. For a
parallel RL circuit, the higher peak in Figure 5.25b dominates in the superposition;
however, for a series RL circuit, the lower peak dominates. This is also consistent with
the shift of the eigenfrequency. Compared to the R only response curve, the curve for the
optimal parallel RL circuit shifts to the left (due to the higher peak in Figure 5.25b); on
the other hand, the curve for the optimal series RL circuit shifts to the right (due to the
lower peak in Figure 5.25b).
5.6. SUMMARY AND CONCLUSIONS
This Chapter presents the development of bio-inspired hair flow sensors based on the
emerging piezoelectric microfibers.
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• To mimic the structure and function of the hair sensors in fish lateral line system,
three designs are proposed: piezoelectric microfiber with surface electrodes,
piezoelectric microfiber with spiral electrodes, and piezoelectric microfiber with
artificial cupula.
• All the three designs lead to both directional sensitivity and linearity. The
directional response follows a cosine function with the direction of the applied
stimulations; in a same direction, the sensors present linear response. These
features are also found in the hair sensors of fish.
• The performance of the hair sensors is modeled using uncoupled analytical model,
as well as using fully coupled numerical model. The sensitivity of the sensors is
proved. With a unique experimental setup, the performance of the sensors is
validated in the laboratory.
• An advantage of the first design is that the fabrication process is relatively
straightforward, whereas it is not durable enough due to the fragile nature of the
PZT microfiber; The second design is much more resistant to fracture and wear,
but the fabrication requires much more efforts and relies heavily on manual
manipulation. It is worth noting that, the two designs utilize different sensing
modes of piezoelectric material. Specifically, the first design utilizes the d31 mode,
and the second utilizes the d33 mode.
• A third design is proposed to address the limitations of the first and second design.
This design is inspired by the structure of the superficial neuromasts of fish,
which is composite structure with the hair cells embedded in a compliant material
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called cupula. The third design is achieved by embedding the piezoelectric fiber
with surface electrodes (first design) into a compliant polymer cylinder.
• To optimize the sensitivity and bandwidth of the sensor with artificial cupula, the
sensor responses, both static and dynamic, are modeled both analytically and
numerically. A unique contribution is the introduction of an innovative approach
to adapt the frequency response of the hair sensor: connecting the sensor to an
external shunt circuit. Optimal design can be achieved based on a systematic
evaluation of the various design parameters.
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CHAPTER 6
A TDR FIELD BRIDGE SCOUR MONITORING SYSTEM
6.1. INTRODUCTION
As discussed in Chapter 1, the severity of the scour has drawn a national-wide attention.
And this leads to mandatory regulations for evaluation and inspection for every over- waterway bridge (National Bridge Inspection Standards, 2004). To this end, an accurate, cost effective, and easy-to-install scour sensor is in high demand.
In addition, scour will be most severe in flood events and bridges will be at high risk of failure during flood events. Hence, real-time scour information is critical for officials to predict the potential evolution of the scour hole and to take immediate action to close the bridges prior to the failure. On the other hand, the flood also threatens the security of the scour sensor itself since it always means extra hydrodynamic loads and huge amount of debris, which may damage the sensors easily. Also, during the flood recession, sediments would probably refill the scoured hole and this sedimentation process should also be identified. Therefore, the ideal field scour sensor should also provide real-time scour information and have to be durable and robust.
Whereas field monitoring is essential for bridge risk management, the field scour data is also particularly useful for calibrating and updating the existing scour prediction models.
Scour prediction formulae are usually functions of characteristics of the bed material,
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bedform, flow and pier configuration. Numerous equations are available for local pier
scour and most of them are based on the laboratory experiments, where all the above- mentioned characteristics are simplified or idealized. For previous editions of HEC-18,
the pier scour equation based on the CSU equation is recommended for scour prediction
(Arneson et al. 2012). However, comparisons with field data revealed that the existing
equations (including the HEC-18 equation) frequently over predicted the scour depth. In the latest version of HEC-18, another methodology is recommended as an alternative
method to the CUS based equation. This methodology is the Florida DOT pier scour
methodology based on the NCHRP equation (or the Sheppard and Miller (2006)
equation), which is proved to perform better for both laboratory and field data (Arneson et al. 2012). However, field scour data is still far from sufficient. Real-time and continuous monitoring of scour at bridges would provide valuable information to improve the prediction models as well as to unveil the underlying mechanism of bridge scour.
To sum up, bridge scour sensors are in urgent need and the ideal sensors should be accurate, cost effective, easy-to-install as well as durable and robust; it should also provide continuous information of the real-time scour/sedimentation process. A number of scour sensors have been designed over the past two decades. The traditional methods include the sounding rods, sonars, tilt sensors, buried or driven rods (e.g. magnetic sliding collar), and other buried devices such as float-out sensors. Such techniques can meet one or several of the above-mentioned requirements but not all of them. All these methods are discussed and summarized in NCHRP and FHWA reports (Hunt 2009, Lagasse et al.
2009). The strengths and weaknesses of such methods can also be found elsewhere
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(Zarafshan et al. 2012). In addition to the traditional methods, we also found some
interesting innovative sensing techniques during recent years. Fiber Bragg grating (FBG)
sensors were applied to detect scour phenomenon directly or indirectly. Scour can be
monitored directly through strain sensing with distributed FBG sensors mounted on a
cantilevered or fixed rod/bar near the bridge piers (Lin et al. 2005, Xiong et al. 2012); it
can also be detected indirectly by relating the natural frequency of vibration of an
embedded rod in the riverbed to the scour depth and the natural frequency of the rod can
be measured using a single FBG sensor (Zarafshan et al. 2012). Direct measurements can
also be realized using distributed pressure MEMS sensors (Lin et al. 2010) or
piezoelectric films (Fan et al. 2007); attempt to relate the fundamental frequency of the
bridge itself with the scour depth has also been made using motion sensors (Chang et al.
2010). Imaging techniques has also been introduced to monitor real-time scour processes.
Chang et al. (2012) developed a multi-lens system which can track scour images and retrieve the scour information through image recognition processes. Extending single point measurement to 3-dimensinal profiling of the bedform around bridge piers has also been attempted using rotatable sonar profiler (Shin and Park 2010).
All of these innovative techniques are encouraging. However, each of the techniques has its own drawbacks. For example, the accuracy of the direct FBG sensor depends on the number of FBG elements in the sensor and the measured scour depth is in a discrete incremental fashion; a main drawback of the indirect methods is efforts should be made to differentiate scour effects from other possible reasons (e.g. ambient perturbations, and traffic) for natural frequency shift of measured structures; turbidity of the flow, especially in flood periods, will definitely present challenges for camera or sonar based techniques.
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In this paper, we present an innovative scour sensor which provides both reliable (direct
measurement) and continuous (real-time) scour information, with little to no affects from the turbid flow. This sensor is a Time Domain Reflectometer (TDR), which is specifically designed for field applications. TDR is based on the guided electromagnetic wave technology; it is super accurate for detection of interface where the dielectric properties mismatch. Scour is a particular interface problem in that the interface between water and sediment defines the scour profile; and the dielectric properties of sediment and water differ from each other significantly. Therefore, it is straightforward to apply
TDR technique to detect the scour process. Dowding and Pierce (1994) proposed to measure scour by detecting the shearing of a coaxial cable by the stream flow and apparently this system is not reusable. Yankielun and Zabilansky (1999) first introduced a TDR probe to identify the sediment/water interface for scour monitoring. While it was proved rugged enough to resist flood/icing damage, the intrinsic design of the probe made it difficult to install in the field, difficult to interpret the signals and limited to a relatively short sensing range. Efforts are made to develop a robust algorithm for scour measurements using the TDR signals (Yu and Zabilansky 2006, Yu and Yu 2006, 2009,
2010, 2011); a more reliable design of the TDR sensor has also been proposed to address the practical issues such as cost, sensitivity, durability and easiness to install (Zhang et al.
2008, Yu et al. 2009, Yu et al. 2013). All these studies paved the way for field application of the innovative TDR sensor for real-time scour monitoring.
This paper presents our latest progress on the in-situ application of the innovative TDR sensor (designed and evaluated by Zhang et al. 2008, Yu et al. 2009, Yu et al. 2013) to advance the state of practice of field scour monitoring. The design and fabrication of this
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TDR sensor is will be first presented briefly, followed by a description of technical basis
of the TDR scour sensor; the field deployment of the sensor and its long term
performance will be emphasized; successes and pitfalls are then discussed; the sensor will
be improved in the future to strengthen the weak points in the whole sensing system and
will be deployed on more bridges across the nation.
6.2. SENSOR DESIGN AND FABRICATION
TDR is a guided electromagnetic wave technology that measures material properties based on the speed and attenuation of electromagnetic waves. It was originally used by
electrical engineers to locate discontinuities in electrical cables; it has been increasingly
adopted by civil and environmental engineering communities for characterization of
geomaterials (e.g., among others, Noborio 2001, Yu and Drnevich 2004). The traditional
and most commercial TDR probes include two or three bare metal rods. TDR encounters
challenges in application to highly conductive materials due to the significant attenuation
of the electromagnetic waves in such materials. This drawback can be compensated by
either shortening or coating the TDR probes (Sun et al. 2000). The latter approach is
adopted in this study. Efforts are also made to design the TDR probe to be ready for
various field applications. This means the TDR probes should be durable, economic, easy
to transport and install as well as accurate and sensitive.
Different from traditional TDR probes which usually consist of separated cylindrical rods,
the proposed sensor is a composite design. It mainly includes 1) three flat metal bars as the wave guide, 2) tapes and adhesive coating to improve its performance in highly
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conductive materials, 3) high-strength E-glass U-channel as the structural support
(Figure 6.1a, 6.1b).
Figure 6.1. The newly designed field TDR bridge scour sensor. (a) The schematic drawing of the cross-
section of the sensor; (b) The longitudinal view of the sensor; and (c) the photo of the fabricated bridge
scour sensor (one portion of the E-glass U-channel is cut to expose the TDR strip).
All the materials are cost effective, and the fabrication process also saves time and efforts.
Three high-carbon stainless steel strips (12.5mm*2.54mm) were first aligned parallel to
each other with spacing of 2mm; the gaps were then filled with Polytetrafuoroethene
(PTFE) Teflon; the top and bottom surfaces were covered with tape and a thin layer of
adhesive coating; the integrated strip wave guide were then completely mounted on the
E-glass U-Channel (50.8mm*14.3mm*3.2mm). The geometry of the strip sensor makes it
close to 50 ohm impedance when exposed to air; this ensures the impedance match to the
coaxial cables. The fabricated sensor is shown in Figure 6.1c and a portion of E-glass is cut off the expose the strip wave guide. It is worth noting that the total material cost for
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the sensor of 20ft long is less than $100; in addition, the cross-section of the sensor is small is enough to fit in a standard geotechnical borehole.
6.3. TECHNICAL BASIS AND PROCEDURE OF SCOUR MONITORING USING THE
INNOVATIVE TDR SENSOR
TDR works by generating a small-magnitude and short-time electromagnetic pulse to the
probes and “listen” to the echoes from materials. As shown in Figure 6.2a, a simple setup
of the TDR system typically includes a TDR sensor, a TDR signal generator and a data
acquisition system. The electromagnetic wave travels with different speeds in materials
with different dielectric spectra. When the sensor is embedded in layered materials, the
mismatch of materials will result in reflections, which can be displayed cleared in the
time domain signal (Figure 6.2b). The dielectric constants for air, water and sands are
approximately 1, 80 and 3. The huge differences between the dielectric properties of
water and sands make it ideal for scour monitoring.
Figure 6.2 shows the laboratory setup of the scour sensing and corresponding sample
signals. In a TDR signal, the time information is displayed by the apparent length La.
Based on the relationships among apparent length, physical probe length in materials (L), and wave speed in materials, the dielectric constant Ka are related to L and La. (Eq. 6. 1,
for details, see Yu and Yu 2006). To determine La, the reflection points can be
determined with the commonly used “tangent line” approach (Yu and Drnevich 2004).
2 La Ka = L (6.1)
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(a)
(b)
Figure 6.2. The laboratory setup of the scour sensing (a) and the sample TDR signals (b). L1, L2, and L is
the thickness of the water layer, the sediment layer and the water and sediment mixture, respectively. La
and La’ is the apparent length of the mixture when the thickness of the sediment layer is 70cm and 5cm,
respectively. The reflection points in the signal are correlated to the interface between two different
materials along the TDR sensor.
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One should note that the measured signals represent the dielectric information of the
whole sensor system, and any material in the sensor’s effective sensing region contributes
to the final signal. In the region (b-d) of the system shown in Figure 6.2a, the
contributive materials include 1) water, 2) soil and 3) non-waveguide materials of the
sensor (e.g., PTFE, coating and E-glass).
For the layered water and soil system, the semi-empirical volumetric mixing model (Eq.
6.2,) was utilized to estimate the apparent dielectric constant of the water/soil mixture
(Eq. 6.3, Yu and Yu, 2006).
j αα (KKmix ) = ∑υi( i ) (6.2) i=1
where Kmix is the dielectric constant of a mixture material; υi and Ki is the volumetric
fraction and dielectric constant of each component of the mixture, respectively.
LL K=12 KK + (6.3) amix,LLaw ,,as
where Ka,mix , Ka,w, and Ka,s is the apparent dielectric constant of the layered water/soil
system, the water layer and the soil layer, respectively.
After normalization, a linear relationship was found between the normalized mixture
dielectric constant and the normalized soil layer thickness (Eq. 6. 4)
KKa,, mix x a s = −11 +=ax + b (6.4) L r KKaw,,aw
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where x and xr denotes the thickness and the normalized thickness of the soil layer,
respectively. A and b are constant which can be obtained using linear fitting of the
measured data.
Through a series of laboratory experiments with different types of sands and water, Yu
and Yu (2006) established a general form for Eq. 6. 4 (Eq. 6.5).
Ka, mix =−+0.43xr 1 (6.5) Kaw,
From Eq. 6. 5, it is apparent that once the dielectric constant of the soil/water mixture
(Ka,mix) is determined, it is easy to find the thickness of the soil layer. For example, in
Figure 6.2b, when the thickness changed (from 70 cm to 5cm), the apparent length also altered (from La to L’a).
As mentioned earlier, the materials of the sensor also contribute to the measured
dielectric constant. To obtain the dielectric constant of the soil/water mixture (Ka,mix) from the matured overall dielectric constant (Ka), Yu et al. (2013) has established a
calibration equation for this particular TDR sensor through experiments (Eq. 6. 6).
2 Ka, mix =−+−0.12 KKa 7.93a 59.50 (6.6)
To sum up, the complete procedure to detect scour using the proposed TDR sensor is
shown in Figure 6.3.
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Figure 6.3. The procedure to determine the scour depth through the TDR signals. (a) The apparent length can be obtained from the reflection points in the TDR signal, which represents the head and end of the TDR
probes; (b) Ka is calculated using Eq. 6.1; (c) Ka,mix is a function of Ka (Eq. 6. 6); (d) xr is calculated using
Ka,mix (Eq. 6. 5); (e) the relative scour depth can be obtained given sediment layer thicknesses at two times.
6.4. FIELD DEPLOYMENT OF THE TDR SCOUR MONITORING SYSTEM
Figure 6.4. Schematic Diagram of the Real-time TDR Field Bridge Scour Monitoring System.
Components ③-⑦ constitute the control unit, which collects and sends TDR data wirelessly, as well as
provides power to the system.
6.4.1. System Design
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As discussed in the introduction section, an ideal field scour monitoring system should
provide real-time scour information. Figure 6.4 illustrates the proposed field scour
monitoring system using the newly designed TDR strip sensor.
The TDR sensors are designed to be partially embedded in the river bed (Figure 6.4①);
thanks to the sensor’s capability for serial multiplexing, several TDR strip sensors can be
installed at different locations in vicinity of bridge abutments or piers at the same time.
The sensors are connected with the field control unit via coaxial cables (Figure 6.4②).
The control unit includes a TDR signal generator (Campbell Scientific® TDR 100) with
a multiplexer (Campbell Scientific® SDMX50) (Figure 6.4③), a data logger (Campbell
Scientific® CR1000, Figure 6.4④), a rechargeable battery (Enersys® NP12-12T, Figure
6.4⑤) with a solar panel (Figure 6.4⑥) and a cellular modem (Figure 6.4⑦). The control unit sends electromagnetic waves to the TDR sensor with the signal generator; it collects the data from the sensors with the data logger and sends them to the internet server via the cellular modem; the data logger can be programed to read TDR data at preset time intervals (e.g. 1 hour). Researchers or officials can visit the corresponding website to check the data with any internet accessible terminals (e.g., PCs, Smartphones and etc.).
The sensors are installed with routine geotechnical investigation equipment and procedures and this will be discussed in detail in the following section; the whole system is powered by the rechargeable battery with energy from the solar panel and the battery and power consumption data can also be monitored in addition to the TDR data; the components of the control unit are integrated in a compact box, which is fixed on the
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bridge deck. All of these features ensure the proposed monitoring system is economic,
efficient and easy for installation and management.
5 4 3
2 1
Figure 6.5. The locations of the installed TDR sensors at the BUT-122-0606 Bridge on State Route 122
over the Great Miami River.
6.4.2. Field Deployment
The bridge under monitoring is the seven-span BUT-122-0606 Bridge on State Route 122 over the Great Miami River in Butler County, OH. According to USGS stream flow statistics, the annual average discharge at this location is about 6,209 ft3/s (USGS
website). And during year 2004 and 2008, there were three major flood events with
discharge over 50,000 ft3/s. Under-water inspections in 2004 and 2007 indicated a significant increase (around 2ft) of local scour around several piers, due to the flood events. The installation of this pilot monitoring station is expected to further provide real-time scour data, which will assist operational decision making and provide information for countermeasure design.
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Five TDR sensors were installed at different piers. The sensors are located approximately
1ft from the corresponding piers and 6ft from the side walk (Figure 6.5); these locations are selected considering the maximum shear stress location and the easiness to install.
The locations of the TDR sensors are shown in Figure 6.5.
The TDR sensors are installed through routine geotechnical site investigation equipment and procedures (Figure 6.6a). The procedure can be summarized as: 1) to locate the equipment at the designed location on the bridge deck; 2) to core through the bridge deck;
3) to drill in the river bed to the design depth; 4) to lower the TDR sensor into the borehole; 5) to backfill the borehole with sand, pull out the assisting borehole casing and seal the coring hole in the bridge deck; 6) to move the equipment to the next location and repeat steps 2 to 5.
(a) (b)
Figure 6.6. (a) Installation of the field TDR sensor using traditional geotechnical equipment and
procedures; and (b) The installed field control unit.
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The field control unit was installed on the bridge near Location 4 shown in Figure 6.5.
All the sensors are connected to the control unit via protected coaxial cables. A pair of
steel pipes was fixed on the bridge to host the housing box (Figure 6.6b). The field
monitoring station is proved to be easy to access as well as protective to the control units.
6.5. LONG-TERM PERFORMANCE OF THE SYSTEM
The field TDR bridge scour monitoring system was installed in September, 2009. Since then, the system has continuously served with encouraging performance. Routine maintenance has been conducted; it is found there are several challenges on the protection of the system. These challenges need to be addressed in order to improve the longevity of the system.
Reflection at the probe 0.2 head 0
-0.2
-0.4
-0.6 Relative Voltage -0.8 Reflection at the probe end -1
-1.2 0 20 40 60 80 100 120 140 160 Length (m)
Figure 6.7. Sample signals of the field TDR sensor. The reflection points and the change of the probe end
reflection are clear.
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6.5.1. Preliminary Data Analysis
Figure 6.7 shows a typical signal from the field sensor. The reflections of the electromagnetic wave at the probe head, water/sediment interface and the probe end are clear. Following the algorithm and procedures elaborated in Figure 6.3, it is straightforward to evaluate the scour evolution through a series of TDR signals.
Table 6.1. Example calculations using the algorithm elaborated in Figure 6.3.
Reflection Reflection Total Incremental Point at the Point at the La Cumulative Day Ka Ka, mix xr x(m) Scour Depth Probe Head Probe End (m) Scour (m) (m) (m) Depth (m)
1 26.29 32.2 5.91 15.04 32.42 0.85 1.30 0.00 0.00
2 26.29 32.3 60.1 15.55 34.60 0.81 1.23 0.07 0.07
3 26.29 32.36 6.07 15.86 35.90 0.78 1.18 0.04 0.12
4 26.29 32.43 6.14 16.23 37.40 0.75 1.14 0.05 0.17
58 26.29 32.03 6.29 17.03 40.56 0.68 1.04 0.10 0.27
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Figure 6.8. Scour evolution at Location 1 during the first two months.
An example of the implication of the TDR scour algorithm is shown in Table 6. 1. The data is sampled at location 1 (Figure 6.5) in the two months after installation. The cumulative scour depth is illustrated in Figure 6.8. It is interesting to observe that the scour developed fast in the first several days after installation and it tended to be stable in long time. The fast growing scour depth in the initial stage is probably due to the disturbance of the local sediments during scour sensor installation; after most of the weak soil was eroded, the scour evolves gradually.
Table 6.2. The cumulative scour depths at the five locations 2 months after installation.
Location Location 1 Location 2 Location 3 Location 4 Location 5
Scour Depth (m) 0.27 0.16 0.41 0.47 0.21
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The scour depths for all the five monitoring locations 2 months after of installation (as shown in Table 6. 2) revealed that the scour depths in the middle spans (i.e. Location 3 and 4) are slightly larger than those at the other locations. This can be explained by the fact that the flow velocity is higher at these locations in the river channel.
(a)
(b)
Figure 6.9. (a)The stream discharge record of the river at the bridge (data from USGS website) between
November 2010 to April 2012; (b) Monitored scour/sedimentation process during the same time-span.
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For a longer time span, the scour data can be related to the stream discharge data and this
is beneficial for future scour prediction. For example, during the winter season in 2010
and the spring season in 2011, the stream discharge record (USGS data, Figure 6.9a) at
the bridge shows periodic flood events approximately at one month intervals. The
discharge reached its peak in March, 2011. Correspondingly, the scour depths at bridge
piers also demonstrated periodic peaks during these three flood events (Figure 6.9b). The
scour was also most severe in the March flood period. It is worth noting that the sedimentation (backfilling) process during the flood recessions is also indicative in the
TDR data plot.
6.5.2. Challenges and Pitfalls
The success of the proposed TDR bridge system shows that it is a promising
countermeasure to scour critical bridges. However, we also encountered some challenges and pitfalls in terms of protection and the long-term performance of the proposed system.
These includes, 1) it was found that the coaxial cable and the cable/sensor connector are
the weak spots of the whole field sensing system. During the field monitoring period,
exposed cables were found to be cut, possibly by vandalism activities. This caused the
loss of two scour monitoring sensors. 2) Impact of debris, such as floating wood trunks,
possesses a major challenge for the system to survive. Although the TDR probe itself is
strong enough to survive the harsh environment, the debris and high flow velocity often
shear the coaxial cables. 3) Occasionally, there are some erratic signals, which is different
vastly from the normal signals. These may be caused by electromagnetic interference due
to lighting system or other sources. But this is relatively a minor issue considering that it is rare.
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To protect the coaxial cable, conduits were used to lead the cables to the control unit. It was found effective to prevent vandalism activities and to endure attack from small debris. However, the cable/sensor connection section is still vulnerable to huge debris in flood events. According to NCHRP survey, the protection of cables was a major concern for several states (Hunt, 2009). Barrier rods were used to protect a FBG based scour sensor in the field (Zafafshan et al. 2012) and were effective preventing impact form tree trunks. But the installation of the barriers into the riverbed may cause extra cost; and big and wide barriers may alter the flow around the sensors and result in inaccuracy for capturing the real scour situation; small and narrow barriers, on the other hand, may provide little protection of the sensor. The protection of the field bridge scour sensing system still needs to be addressed creatively in the future.
6.6. SUMMARY AND CONCLUSIONS
Bridge scour is a major threat to the health of the bridge and it evolves fast in flood events. Field bridge scour sensors are expected to provide real-time scour information as well as to be accurate, cost effective, easy-to-install and durable. The contributions of this study include:
• A remote bridge scour sensing system with a newly designed TDR probe is
designed and implemented in the field. The TDR sensor is a composite sensor
which is made of durable and inexpensive materials; a robust algorithm is
developed to retrieve scour information from TDR signals.
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• The field system includes the TDR sensors, TDR signal generators, data logger,
and wireless modem; it is powered by a rechargeable battery which is charged
using a solar panel.
• The TDR sensors are installed using traditional geotechnical investigation
equipment and procedure. The signals from the sensors are acquired by the
control unit at preset time intervals and wirelessly transmitted through cellular
data service. It was proved that the field TDR sensor system and the proposed
algorithm are capable to provide real-time scour and sedimentation information.
• Challenges also exist in terms of improving the longevity of the system. While the
TDR sensors are robust enough to survive the harsh field environment, the cables
are found to be the weak spot in the whole system. Efforts are needed to provide
enough protection to the cables in the future. Also worth exploring is to
incorporate the field sensing data to risk-based bridge management as well as to
improve the existing scour prediction formulae, which are mostly developed
based on laboratory data.
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CHAPTER 7
SUMMARY, CONCLUSIONS AND FUTURE WORK
7.1. SUMMARY AND CONCLUSIONS
Bridge scour accounts for almost 60% of all the bridge failures in United States. Its
mechanism is still not fully understood due to its complexity, involving the interactions
among structure, flow, sediments and bedform. These interactions lead to problems such
as the pattern of turbulence structures around bridge piers (flow-structure interaction), the sediment transport and the influence of turbulence on it (flow-sediment interaction), the dynamic evolution of the scour hole around bridge piers (flow-sediment-bedform interaction). This dissertation work presented the efforts to advance the research and practices on bridge scour by addressing challenges related to aforementioned problems. It is also worth noting that intense effort is made to review the state-of-knowledge, state-of-
art and state-of-practice literatures on the bridge scour modeling and bio-inspired hair
sensor development. The existing knowledge on these topics is synthesized and this part
of work does not only provide a reference to other researchers but also has guided this
dissertation work to some extent.
7.1.1. CFD modeling of the effect of pier configurations on flow and scour pattern
CFD technique is applied to simulate the flow patterns around bridge piers with different
configurations. The effects of various pier configuration factors are assessed. It reveals
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that for piers with blunt noses, there exists a strong downward flow; for piers with sharp
noses, however, the downward flow is much weaker. Attack angle also influences the
flow patterns dramatically. When the attack angle is zero, the aspect ratio of oblong piers
does not affect the overall flow patterns significantly, but it indeed has influence on the
interaction between different vortex structures.
The simulated flow patterns are then compared with scour patterns. It can be concluded
that the maximum bed shear stress locations are always consistent to the maximum scour
depth locations. But the overall pattern of the scour hole is not always consistent with the pattern of shear stress. For example, in front of square piers, the scour hole is considerably deep while the bed shear stress in that region is relatively small. For oblong
piers with different aspect ratios, although the overall pattern of the bed shear stress is
consistent, the scour hole pattern is dramatically different from each other.
Traditionally, the bed shear stress is considered as the only reason responsible for scour.
But based on the modeling and comparison results, it indicates that the downward flow
and the interactions among different vortex structures might also play a great role in the
process of scour.
This study also has practical implications and the findings can be utilized to guide the
design of countermeasures and monitoring plan for bridge scour practice. For example, since the maximum shear stress locations always indicate the maximum scour depth locations, the CFD technique can be utilized to aid the design of the monitoring plan. The long-term monitoring sensors are always expected to be located at the most possible
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maximum scour depth locations. The calculated shear stress patterns can be utilized to
design the layout and sizing of the riprap for scour countermeasures.
In addition to the simulation of flow patterns alone, a framework for modeling of the
scour evolution process is also proposed and a unique contribution is that the influence of
turbulence on sediment transport is considered. But future implication and validation of
the proposed framework is required.
7.1.2. Bio-inspired hair flow sensor
In order to advance the understanding of the initiation and transport of the sediment
particles, the characterization of turbulence structures, especially those in the same scale
as the particles, is a prerequisite. For this purpose, innovative flow sensors are designed,
which are inspired by the hair cells in fish.
Mimicking the function and structure of the hair cell sensors, three designs based on
piezoelectric materials are proposed, modeled, fabricated and evaluated. Through
patterning the electrodes, two designs were proposed: one is with a pair of surface
electrodes deposited directly on the piezoelectric fiber and this design mainly utilized the
d31 mode of the piezoelectric effect; the other is with a pair of spiral conducting wires
attaching on the surface of the fiber and this design is working in the d33 mode. The linear response and directional sensitivity are achieved through both of the two designs. The fabricated sensors in macro scale are evaluated in a unique laboratory setup and the linearity and directional sensitivity are validated. It is worth noting that the directional sensitivity follows a cosine function with the loading/flow direction, which is identical to that of hair cell sensors in fish.
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Both of the two designs have obvious drawbacks: the first design is fragile and the
second design relies heavily on tedious manual fabrication. Inspired by the cupula of
superficial neuromasts of fish, a composite design is proposed. The piezoelectric microfiber is embedded within certain polymer cylinders to improve the entire flexibility and durability of the sensor. The sensitivity of the composite sensor significantly depends on the material of the polymer and to achieve optimal sensitivity, the mechanical properties of the polymer and the piezoelectric fiber should be matched.
A unique approach, introducing a shunt circuit to the sensor, is first proposed to adapt the
frequency response of the artificial hair cell sensor. The effects of circuits with different
configurations on the dynamic response of the sensor are evaluated using a fully coupled
mechano-electrical-circuit model. The introducing of the shunt circuit increases the
damping of the sensor by dissipating part of the kinetic energy: reducing the peak sensitivity and shifting the eigenfrequency. Different circuit components, namely the resistor and the inductor, and different configurations, namely in parallel and in series, have different effect on the damping. The most significant damping occurs when an optimal resistor is connected with an optimal inductor in series.
7.1.3. TDR field bridge scour monitoring system
A TDR field scour sensor is successfully deployed at a field bridge site in order to provide real-time scour depth information. The field system includes the TDR sensors,
TDR signal generators, data logger, and wireless modem; it is powered by a rechargeable battery which is charged using a solar panel.
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The sensor is a composite sensor which is made of durable and inexpensive materials; a
robust algorithm is developed to retrieve scour information from TDR signals. The TDR
sensors can be installed using traditional geotechnical investigation equipment (driller)
and procedure. Wireless transmission of the TDR data is realized using the cellular data service. It was proved that the field TDR sensor system and the proposed algorithm are capable to provide real-time scour and sedimentation information in the real riverine
environment. Such data can be utilized to calibrate the various scour depth prediction
equations. It can also be integrated into the bridge risk management system to assist in
decision making.
7.2. FUTURE WORK
While tremendous efforts have been made to complete this dissertation work, there remain a lot of inadequacies which deserve further investigations. The short-term future
research will aim to consummate the CFD scour models and improve the design for both
the hair sensors and the field scour sensor. The long-term goal is to build an integrated
system for bridge scour risk management. This system integrates the information from
turbulence data and scour depth data from the field; such information can be utilized to
calibrate the CFD model. With hydrology data, the validated CFD model can be
employed to predict scour depth and to aid the optimal design of the pier configurations,
countermeasures and monitoring plans.
7.2.1. On CFD modeling
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Many fundamental questions on the mechanism of bridge scour are worth investigating.
For example, solving questions such as when and how particles are scoured, how they are
transported, etc., helps to unveil the underlying mechanism of scour.
More studies should also be conducted on the effects of structure geometries. For
example, flow and scour patterns around pier arrays and piers consisting of pile groups with different configurations are limited to experimental studies in laboratory scale,
advanced numerical simulations are expected to provide more implications to the
mechanism of scour around complex structures and thus help to improve the design of
bridge foundation and scour countermeasure.
Simulations coupling eddy-resolving methods, especially DES, to advanced sediment
transport models are the future trend in the area of the scour process simulation. However,
due to its huge demand on computational resources, its application is limited to the very
beginning stage of scour around piers in flow with a medium Reynolds number (e.g.
3.9×104) (Escauriaza and Sotiropoulos, 2011a). In the future, we are expected to see more
researches on scour at various stages and in flow with higher Reynolds numbers which
are close to real life river conditions.
7.2.2. On biomimetic flow sensor
The sensor prototypes presented in this dissertation were only fabricated in the macro scale. The next step of the research is to further scale down the sensor design. The rapid growth in fabrication technologies such as Nano Electro-Mechanical Systems (NEMS) technique shows great potential in the development of bio-inspired sensors in the same scale of their biological counterparts. For example, piezoelectric nanowires have been
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successfully fabricated (Gao and Wang 2007, Wang 2011, Lin et al 2009) and could be utilized in the scaling down of the proposed sensor. Other piezoelectric materials besides
PZT are also worth exploring if they have higher sensitivities. For example, emerging piezoelectric nanocomposites are promising smart materials for novel sensors. These include, for example, CNT/PVDF composites (Dai and Ohashi 2010), CNT/epoxy
composites (Wichmann et al. 2008), CNT/ZnO composites (Mason 2009, Hu et al. 2011),
which all show enhanced performance compared to pure piezoelectric materials.
Besides the various aspects on single sensor development, data acquisition, information
processing, interferences or viscous-coupling occurring in sensor arrays are also vital to a
biomimetic flow sensing system. Comprehensive understanding of the biological sensing
systems including their sensing ability, the sensing components and sensing principles,
and the factors influencing their sensitivity (such as geometries and distributions) will
build the basis in the design of successful biomimetic flow sensors.
7.2.3. On field bridge scour monitoring system
Challenges also exist in terms of improving the longevity of the field bridge scour
monitoring system. While the TDR sensors are robust enough to survive the harsh field
environment, the cables are found to be the weak spot in the whole system. Efforts are
needed to provide enough protection to the cables in the future. Also worth exploring is
to incorporate the field sensing data to a risk-based bridge management process as well as
to improve the existing scour prediction formulae, which are mostly developed based on
laboratory data.
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