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