Physical Modelling of Concentration Fluctuations in Simple Obstacle Arrays
Robert Macdonald and Brian Kim Department of Mechanical EngineeringUniversity of Waterloo, Ontario, Canada
Eric Savory Department of Mechanical and Materials Engineering
University of Western Ontario, Canada
Miho Horie and Shiki OkamotoShibaura Institute of Technology, Tokyo, Japan
Presented at NATO ASI, May 2004
Content• Background • Description of the physical modelling facility
- Hydraulic flume- Atmospheric boundary layer simulation- Obstacle arrays
• Planar Laser Induced Fluorescence (PLIF) technique for concentration measurements
• Discussion of results for- Mean concentrations- RMS concentration fluctuations
• Conclusions
Air Pollutants• Local stack plumes• Exhausts from
automobiles• Accidental Releases
Street Canyon
• The canyon flow is affected by the arrangement and spacing between the buildings
• Geometry created by a narrow street with buildings lined up continuously along both sides (Nicholson, 1975)
Background
Concentration fluctuations can be important in assessing toxic risk.
Experimental data on concentration fluctuations in obstacle arrays is quite sparse.
It has been suggested that Crms is O(Cmean) but estimates vary greatly.
The present study seeks to quantify Crms / Cmean
for different obstacle arrays and downwind locations.
Objectives
• Obtain concentration profiles using PLIF technique in a water flume
• Determine the effects of obstacle configuration on mean dispersion parameters (max. concentration, plume height, etc.)
• Obtain relative concentration fluctuation intensity profiles
• Validation of PLIF application
Scale Modeling• Full-scale (field) and Small-scale Studies
• 10 m : 5 cm = 200 : 1
Experimental Facilities (I)
• Hydraulic Flume– Fully developed, turbulent approach flow
(10cm/sec)
- Flume dimensions: 12.6 m x 1.2 m x 0.8 m
2.4 m
Experimental Facilities (II)
• Light Source System
– Argon ion Laser (Maximum, 5W)
– Fixed frequency resonant optical scanner
– 1 mm Light sheet
0
10
20
30
40
50
60
70
0 5 10
U (cm/ s)
Z (cm
)
X=0cmX=50cmX=100cmX=147cm
Approach Flow Characterization• Acoustic Doppler
Velocimeter (ADV: 20 Hz)
Reference Height (5cm)Zo = 0.20 mm (0.4 m FS)UH = 5.74 m/sU* / UH = 0.13 = 0.29 Suburban terrain
0
2
4
6
8
10
12
14
0 0.2 0.4
σ i/UH
Z/H
σ u/uHσ v/uHσ w/uH
0
2
4
6
8
10
12
14
0 0.2 0.4σ i/UH
Z/H
σ u/uHσ v/uHσ w/uH
• Non-dimensional Turbulence Intensity
X = 0 cm X = 50 cm
0
2
4
6
8
10
12
14
0 0.2 0.4σ i/UH
Z/H
σ u/uHσ v/uHσ w/uH
0
2
4
6
8
10
12
14
0 0.2 0.4σ i/UH
Z/H
σ u/uHσ v/uHσ w/uH
X = 100 cm X = 147 cm
• Longitudinal > Lateral > Vertical turbulence Intensity
Dispersion Parameter (I)
• Non-Dimensional Concentration (Kc)
Q
H UC K
2H N
C
Where CN = C/Cs
Q = Volume flow rate
UH = Velocity at H (5cm)
Cs = Source conc.
Can be directlycompared with
non-dimensional datafrom
field-scale experiments or
dispersion data fromother wind tunnel
facilities
DispersionParameter (II)
• Net vertical plume variance
Vertical rise of the plumeis a combination of two factors;
The centre of the distribution Zc and the standard deviation of the distribution Z
Reference : Lecture Not (Air Pollution)
C (z)
Z/Hz/H
222
ZCZZ
Experimental Configuration (I)• Square and Staggered Building Array
Experimental Configuration (II)• Unobstructed plume
- Less dilution than in the obstacle arrays higher concentrations - A baseline case for comparison to the obstacle (building) array results
“Lego”roughness Nuts
• 2-Dimensional with different Area Density
Experimental Configuration (III)
xyT
Ff S LS W
WH
A
A
H2 / (2.5Hx2.5H)= 16%H2 / (1.5Hx1.5H)= 44%
1.5 H 0.5 H
AF = Frontal area AT = Total plan area
Previous work with these arrays
• ADV measurements of mean velocity and turbulence quantities, Carter (2000), Macdonald et al (2002).
• Correlation of turbulence quantities above obstacles with: u / U* = 2.10, v / U* = 1.65 and w
/ U* = 1.20.
• Peak TKE about 30% greater above staggered array when compared to square array.
• Value of about 50% larger for flat plate arrays compared to cube arrays.
uw
• 3 different heights (0.3 H / 0.5 H / 1.0 H)
Source Release System
Upstream source (spacings from f = 16%)
Source Types and Downstream-Scale
1 row 2 row 6 row4 row
2.25H4.75H
9.75H14.75H
Inside source
U
U
Summary of Experiments
Source Types Upstream Inside
Array Types
Square
Staggered
TwoDimensional
With NUTS and LEGO
16 %
16 %
16 %
44 %
33 % 44 %
Unobstructed
16 %(Source Height 0.3H,0.5H,1.0H)
16 %
16 %
Traditional Point Measurement Techniques
• Allow measurement of
- Transport processes- Spatial distribution of concentration and velocity
Optical Measurement using Planar Laser Induced Fluorescence (PLIF)
38 33 27 27
58 38 30 33 23 15
57 47 41 35 25 5
56 46 40 35 25 13
58 48 40 33 23 11
55 45 37 28 18 17
57
77 71 65 67 55
76 76 70 65 65 53
78 78 70 63 63 61
75 75 77 68 58 57
95 95 83
99 99 93 81
97 98 98 87
• Digital CCD camera- Whole field measurement
• Indirect measurement - Using dye (as tracer)
• Non-intrusive- Optical technique
PLIF Components
• The basic PLIF system
1. Planar laser light source
2. Fluorescent tracer release system
3. Digital image acquisition and storage system
4. Digital image analysis software
1
2 3
4
Inside test section of water flume
PLIF Principle• Allows measurement of the spatial distribution
of tracer concentrations• The higher the
concentration (C) of dye, the greater the intensity of emitted light (E) for a given intensity of incident light (I):
= calibration const.(e.g. Crimaldi & Koseff, 2001)
CIE
Low-Pass Filter• In the experiments, only the fluorescent
colour (555 nm) of dye is visible to the CCD camera – the use of a filter removes background
argon-ion laser light (514nm)
Wavelength Characteristic
0
20
40
60
80
100
200 300 400 500 600 700 800
um
%T
Calibration
0.5 0.25 0.1 0.05 (ppm) KNOWN Concentration
• To obtain the actual concentration, a calibration box was used with known concentrations of dye to form a calibration curve
• PLIF technique requires a careful calibration to convert image intensity to concentration.
Data Analysis Procedure
Set-UpExperiment
Configuration
ImageRecording
In each ROI
CalibrationBox
Image Record
Experimental Work Image processing
ImageGrabbing
CalculatingConcentration
WithCalibration
CollectingConcentration
Profile Data
Data Analysis
MeanConcentration
UsingGaussian C.Fit
ExtractDispersionParameter
AnalysisOf
RelativeConcentration
• Instantaneous Images : 1st ~ 20th ( 15 sec interval )
Image Gathering
Average Image
20
1N
N/20I
• Fluctuating concentrations:
= -
FluctuatingConcentration
( C )
InstantaneousConcentration
( C )
MeanConcentration
( C )= -
Average ImageInstantaneous ImageTurbulence Image
Turbulent Image Manipulation
• Turbulence Variance( )
• Turbulence RMS ( )
2)'(1
CN
N
1
Fluctuating concentration Image
2)'(C
Variance ( )
RMS ( ) Mean (C)
Concentration Data Analysis
6.5 6.5 10.9 15.1 11.1 15.1 5.3 5.3 9.3 8.4 9.4 14.7 5.9 5.9 9.4 15.1 11.1 11.1 1.4 1.4 7.4 10.9 10.9 11.7 4.4 4.4 9.3 9.1 9.1 11.1 5.8 5.8 8.4 9.4 9.4 11.7
78 78 83 87 87 88 78 78 80 83 83 85 77 77 81 85 85 85 76 76 80 85 85 83 78 78 80 83 83 81 75 75 77 78 78 77
Concentration
ImageIntensity
Number of Images for Analysis
Z/H = 1
• No significant influence of image sample size on the Average image for Cmean
Present Study
• Appropriate sampling time = 5 minutes to ensure
reliable data for Concentration fluctuations Crms
Z/H = 1
1st Canyon Profiles for different image samples
Gaussian Mean Concentration Profiles
Cmean / Cs
0 2x10-3 4x10-3 6x10-3 8x10-3 10x10-3 12x10-3
Z/H
0
1
2
3
4
5
50 images (5min)20 images (2min)10 images (1min)20 images (5min)
RMS Concentration Profiles
Crms / Cs
0 1x10-3 2x10-3 3x10-3 4x10-3 5x10-3
Z/H
0
1
2
3
4
5
50 images (5min)20 images (2min)10 images (1min)20 images (5min)
Relative Concentration Profiles
Crms / Cmean
0 2 4 6 8
Z/H
0
1
2
3
4
5
50 images (5min)20 images (2min)10 images (1min)20 images (5min)
Results
• Mean Concentration Profiles• Non-Dimensional Concentration• Analysis of characteristics for the various area
densities and configurations• Concentration fluctuation profiles
AveragingPartitioning
• Mean concentration profiles
- Each canyon was divided into 5 sections
Mean Concentration Image
• Spatial Averaged Concentration
- Upstream Staggered 1st Canyon Example
0.0006 0.0006 0.0006 0.0006 0.00060.0005 0.0006 0.0006 0.0005 0.00060.0006 0.0005 0.0005 0.0005 0.00050.0005 0.0005 0.0005 0.0005 0.00050.0006 0.0006 0.0005 0.0005 0.00050.0005 0.0004 0.0005 0.0004 0.00040.0005 0.0005 0.0005 0.0005 0.00050.0005 0.0005 0.0005 0.0005 0.00050.0005 0.0005 0.0005 0.0005 0.00050.0005 0.0004 0.0005 0.0005 0.00040.0005 0.0005 0.0005 0.0005 0.00050.0005 0.0005 0.0006 0.0006 0.00070.0008 0.0009 0.0013 0.0007 0.00100.0021 0.0018 0.0023 0.0018 0.00200.0037 0.0037 0.0038 0.0031 0.00350.0080 0.0063 0.0051 0.0052 0.00500.0093 0.0081 0.0076 0.0071 0.00660.0099 0.0097 0.0101 0.0096 0.00740.0099 0.0107 0.0115 0.0105 0.00790.0108 0.0114 0.0100 0.0098 0.0089
Spartial Averaging
0
0.002
0.004
0.006
0.008
0.01
0.012
0 20 40 60 80 100 120
Inside Canyon(pixel)C
/Cs
Average_P 100_Point
100 pixels 20 pixels 20 pixels
0.0077(at Z/H=0.7)Average
• Mean concentration profile fitted with Gaussian curve
0 0.05 0.1 0.15 0.2 0.25 0.3
0
1
2
3
4
1
2
4
6
G 1
G 2
G 4
G 6
2
2
2
2
2
2
2
)(exp
2
)(exp
2exp
2),(
z
c
z
c
yzyp
zzzzy
U
QzyC
C(z)
Z / H
(ppm)
• Saturation, Attenuation, Non-linear regression , Distortion, Reflection, Images for analyzing
Control Factors
– Source concentration (24.5 ppm)
– Small aperture (narrow field of view)
– Weak dye ( C <= max ~ 0.5 ppm)
– Gaussian curve fitting parameters
– Maximum length of camera position (3.8 m)
– Painting all blocks black
– 5 minute sampling with 20 images is optimal
Summary of considerations
0.5 ppm
I. Comparison of dispersion parameters (Kc, Zbar)with
Wind tunnel and Point measurement data
• Different configuration for two experiments
1. Wind T : Ground level release Point measurement at centre of canyon
2. Flume : 0.5 H release, at centre of canyon
Upstream Square Array f = 16%
Nondimensional Concentration (K)
X / H
0 2 4 6 8 10 12 14 16
Kmax(Z=0.5H)
0.01
0.1
1
10
S.Carter (2000)Present Study (2004)Macdonald (1997)
Point Measurement
Wind Tunnel Measurement
Upstream Square Array f = 16%
Mean Height of Plume (Zbar)
X / H
0 2 4 6 8 10 12 14 16
Zbar
(Zc2+z2)1/2
0.4
0.6
0.8
1.0
1.2
1.4 S.Carter (2000)Present Study (2004)Macdonald (1997)
Point Measurement
Wind Tunnel Measurement
II. Analysis of dispersion parameters Kc, Zbar
With
MEAN CONCENTRATION
Upstream Source (f = 16%)
Mean Height of Plume (Zbar)
X / H
0 2 4 6 8 10 12 14 16
Zbar
(Zc2+z2)1/2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
UnobstructedSQUARESTAGGERRED2-Dimensional
Initial plume disperses most rapidly for 2D array and least for square array.
Similar trends for inside source.
Upstream Source (f = 16%)
Nondimensional Concentration (K)
X / H
0 2 4 6 8 10 12 14 16
Kmax(Z=0.5H)
0.1
1
10UnobstructedSQUARESTAGERRED2-Dimensional
Resulting concentrations lower for 2D canyon compared to others.
III. Analysis of fluctuating concentrations
With
Relative CONCENTRATION (Crms/Cmean)
Crms / Cmean
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Z/H
0
1
2
3
4
5
1st Canyon2nd Canyon4st Canyon6st Canyon
• The peak of the relative concentration fluctuation intensity (Crms/Cmean) occurs in the mixing layer immediately above the obstacles
• The ratio
(Crms/Cmean) decreases rapidly below rooftop height.
Relative Concentration Profiles
UpstreamSquare 16 %
Effect of Array Types Crms/Cmean
1 st Canyon
Crms
/ Cmean
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Z/H
0
1
2
3
4
5
Square 16%Staggered 16%
Staggered array shows greater relative concentration fluctuations than the square array both inside and above the canyon.
Effect of Array Types Crms/Cmean
6 th Canyon
Crms
/ Cmean
0.2 0.4 0.6 0.8 1.0 1.2
Z/H
0
1
2
3
4
5
Square 16%Staggered 16%
These differences also seem to occur further downstream, except within the canyon.
2-D Relative Concentration Crms/Cmean
1 st Canyon
Crms
/ Cmean
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Z/H
0
1
2
3
4
5
2D 16%2D 44%Inside 2D 16%
Caton et al (2003)Single cavity, W/H = 1
0.44
W/H=1.5W/H=0.5
• Within the lowest 0.8H of the canyon Crms / Cmean = 0.25 to 0.45 and does not decrease in the downwind direction for the canyons studied. Magnitudes are consistent with Caton et al (2003) and Pavageau and Schatzmann (1999) for 2-D canyons.
• Peaks up to Crms / Cmean = 1.7 occur in shear layer above 1st canyon, decreasing to 0.9 further downstream.
• Further analysis of relative concentration profiles is required (develop model to predict the shape).
Summary
Acknowledgments
Natural Sciences and Engineering Research Council, NSERC (Canada)
Zhiyong Duan
Dr Dubravka Pokrajac for lending me her notebook PC …… I hope it still works !!
Presented in fond memory of Robert Macdonald
1961 - 2004