- Email: [email protected]
Long-term air quality statistics derived from wind-tunnel investigations
Pergamon
Armo\phcrir Enwronmenr Vol. 28. No. I I. Pp. 191>1923. 1994 Elsewcr Science Ltd Printed in Great Britain. 1352-2310194 f7.00+0.00
LONG-TERM
AIR QUALITY WIND-TUNNEL
STATISTICS DERIVED INVESTIGATIONS
N. J. TNO-Institute
for
Environmental
and
DUIJM
Energy Technology The Netherlands
(IMET),
P.O.
Abstract-Wind-tunnel investigations are commonly used to determine vicinity of buildings. Results of these investigations should be comparable used to express air quality standards. An analysis method for wind-tunnel data is proposed which enables distribution of pollutant concentrations which is compatible with the outcome IS long-term averaged concentrations as well as percentile values trations. The method takes into account the lack of horizontal meandering the real atmosphere and the effect of wind speed. Key
lord
it1de.c
Averaged
concentration,
frequency
distribution,
INTRODUCTION
Netherlands air quality standards are expressed as yearly averaged values and “percentile values”. The standard for e.g. NO2 is 9%percentile 135 pg me3, 99.5 percentile 175 pg rnm3, based on hourly mean values (i.e. 135 pgrnm3 should not be exceeded in 2% of the hours per year, 175 p’grnm3 should not be exceeded in 0.5% of the hours per year). In general. air pollutant levels are a result of background pollution levels, i.e. due to sources in the wide surroundings, and of local pollution sources. In order to decide whether the contribution of additional local sources is acceptable in terms of air quality. predictions
need
to
be made.
wind-tunnel
This
paper
measurements deals
wind-tunnel
data
information
on
tional
Model”
with
the
should analysis
necessary air
quality
to
obtain
consistent
be used.
requirements the with
of
required the
Box
342. 7300 AH
pollutant concentrations in the and compatible with the format the calculation of the frequency Dutch “National Model”. The based on I-h averaged concenin the wind tunnel compared lo
percentiles,
wind
“Na-
guidelines.
OUTLINE
OF THE
“NATIONAL
speed,
building
effects.
Predictions of the LTA concentrations are made using the “narrow plume” assumption, i.e. assuming that plumes are within a sector of 30” and that the wind direction probability within each sector of 30” is uniform. The basic Gaussian plume formula for the LTA concentration at ground level (x, y) from a source at origin (0. 0, H) is:
exp[- H*/(2&)1
(1)
where
The recommendations SHORT
Apeldoorn,
S is the stability class N is the wind speed class Q is the yearly averaged source strength (kgs-‘) .f is the probability of wind direction 0 (when point (I. ~1)is downwind of the source), stability S and wind speed class N Us is the representative wind speed for class N(m s-‘) cr,S is the vertical dispersion coefficient for stability class S, (~,.s is an empirical function of downwind distance x(m) II is the number of wind direction sector (for 30 sector, n= 12) I downwind distance from source (m) H plume height (m).
For free-standing stacks on flat terrain, predictions can be made using Gaussian plume models. In the Netherlands. a recommended guideline. generally known as the “National Model” is used to predict the contribution of local sources to yearly averaged concentrations and percentile values in simple situations. Although the “National Model”. includes a guideline for dispersion calculations around a cubic building. for reliable air quality predictions in built-up environments
FROM
l
MODEL”
l
GUIDELINES
include:
description of stability and the empirical functions of coefficient 0,; models to calculate H from long-term statistics of j(0, meteorological stations.
wind speed classes; the vertical dispersion
The “National Model” guidelines (Commissie Onderzoek Luchtverontreiniging. hereafter named COL, 1976, 1981, 1984) describe the prediction of:
l
l long-term 0 percentile
The section of the “National Model” dealing with the prediction of percentile values is generally known
averaged (LTA) values.
l
concentrations 1915
AE 28:11-H
plume rise; S, N) for two Dutch
1916
N. J. DUIJM
as the “long-term frequency distribution” (LTFD) model (COL, 1981; Guldemond*and Bakker, 1986). The LTFD model calculates frequency distributions of 1 h averaged concentrations based on LTA values in wind direction sectors of 5 degrees and on the frequency of occurrence of the wind direction corresponding to each of those sectors. Assuming a two-parameter log-normal distribution in each sector, the frequency at which a defined concentration is exceeded in a sector can be calculated from the sector averaged value and the geometric standard deviation (GSD, the standard deviation of the frequency distribution of log(concentration)), of the concentration distribution in that sector. For reasons of simplicity, the model assumes that the GSD is the same for every sector. Taking into account the frequency of occurrence of every wind direction, the overall frequency at which the defined concentration is exceeded can be calculated. The concentration that will be exceeded in a defined period of time, e.g. 5% (the 95-percentile), can then be computed through an iteration procedure. In the model a value for the GSD of 0.7 is suggested for chemically inert components; this value was found to be applicable in test runs with SOz (COL, 1981). The generality of this value might be doubted (Guldemond and Bakker, 1986). In order to transform the LTA concentrations (based on 30” sectors) to the 5” sector, the lateral dispersion coefficient uys is used. Empirical values for gys as a function of x are recommended. These dispersion coefficients describe hourly averaged plumes. The correct use of the LTFD model is (a) to determine the yearly averaged concentration wind rose of background concentration (at 5” sectors) from routine air quality measurements; (b) to calculate the required percentile value of the background concentrations using the LTFD model; (c) to add the concentration wind rose from the new source under consideration to the background; and (d) to calculate the percentile value of the total concentrations. The difference between the results of steps (d) and (b) is the increase in the percentile value.
If, for example, hourly averaged plumes need to be simulated, additional meandering or wind direction fluctuations that occur on time scales between the averaging time corresponding to the wind tunnel simulation and the required averaging times (e.g. 1 h) can be described by a Gaussian probability density distribution with standard deviation ee P(v)=-
1‘p2 1 I ---
J&ueexp
Here, ‘p is the deviation of wind direction from the hourly mean wind direction. The hourly mean concentration at location (x, y) can be constructed for a flat terrain from the windtunnel data by m Chow k Y) =
GvT(x. y-cp.-u).p(cp)dv.
MEAN
CONCENTRATIONS
WIND-TUNNEL
DERIVED
-m
ev
(4)
Here, U is the mean convection velocity of the plume, and/(z) describes the vertical distribution of the concentration. The solution of this convolution integral is
-! i
FROM
” 2 a;wr+xza;
I (5)
MEASUREMENTS
The width of a plume over flat terrain can be described by the dispersion coefficient cry. The dispersion coefficient is not only a function of distance and atmospheric stability but also of averaging time (see e.g. Builtjes, 1982). When similar plumes are measured in wind tunnels, plume width is normally independent of averaging time. This means that wind-tunnel simulations only represent plumes of a certain averaging time, depending on the scale factor and wind-tunnel characteristics. For most wind-tunnel simulations, this will be of the order of a few minutes.
(3)
If Cwr(x, y) can be described in terms of a Gaussian plume with lateral dispersion coefficient eYwT, this can be written as:
x.f(z) .exp HOURLY
(2)
2.6
From this, it follows ueJz=+ x
(6)
cry, the full-scale hourly averaged dispersion coefficient, can be derived from empirical data or recommended values (COL, 1977, 1981, 1984). uYwT is to be measured from dispersion experiments in a wind tunnel with an undisturbed boundary layer. Instead of uY. direct measurement of wind direction variations at full scale can be used. For wind-tunnel values direct measurement of uywT from dispersion
1917
Long-term air quality statistics experiments is recommended for better accuracy and reliability. The information obtained can now be used for the correction of wind tunnel measurements of dispersion affected by obstacles. A “wind rose” of concentration should therefore be measured. The resolution of measurements should be of the order of 5”. Those measurements can than be corrected according to
canopy + L 5 m ---
-----
1
+ J-n:
which is approximated
by
--.
! I
ChO"A@)=
f: i=-n
-
I
JiYUe
T
sample point 14 I
xexp{-p$}
x Cwr(O + i Aq).
/
c!/3
t
1.5 m.
(8)
'
I
’
I/a 'I
Here, Acp is the wind direction difference between subsequent wind-tunnel measurements. This method can be called “overlapping modelling by calculation”, see e.g. Ide er al. (1991).
Evample 1 The methodology described above is illustrated by measurements of the dispersion of hydrocarbons due to the filling of fuel tanks at petrol stations. The configuration is shown in Fig. 1, the canopy is at a height of 4.5 m. The sampling points are at a height of 1.5 m; sampling point 14 is at the edge of the canopy. Wind-tunnel tests at scale 1 to 100 were carried out at TNO-IMET’s wind tunnel No. 2. The roughness length z,, of the boundary layer was 2 x 10m4 m, the wind speed at 100 mm was 8 ms-‘. The source emission was 6.4 x 10m6 m3 s-’ with 2% tracer gas (isobutylene). Figure 2 shows the measured concentration at the sampling point as a function of wind direction. The correction for meandering is also shown. For this case cB is 52, derived from measurements of plume width in the wind tunnel at 1540 mm (152 mm) and recommended values of uY for neutral stability c7Y= 0.470 .P90’ . zy As could be expected, inclusion of meandering leads to lower peak concentrations and wider plumes. In this case, the recommended value of CT~for neutral stability was used. At sufficiently high wind speed dispersion around buildings will be dominated by mechanically induced turbulence, which justifies the use of neutrally stratified boundary layer wind tunnels for the prediction of long-term averaged concentrations near obstacles. However, large-scale meandering depends on stability and lateral dispersion coefficients for all stabilities should therefore be used, weighted with the
Fig. I. Configuration of example 1, dispersion of benzene at a petrol station. relative frequency of occurrence in question. THE
EFFECT
OF WIND
for the wind direction
SPEED
AND
WIND
SPEED
STATISTICS
Concentrations depend on wind speed. The longterm averaged concentration therefore also depends on the wind speed statistics. Wind speed statistics in the Netherlands can be reasonably well described by a Weibull distribution: (Wieringa and Rijkoort, 1983) p(U>U,)=exp
{
$ (
k >I
(9)
Here, a is known as the scale factor, and k is known as the shape factor (Fig. 3). If within a wind direction sector, wind speed classes i are defined by lower limit Ui-l and upper limit Vi and the concentration Ci for every class is also known, the long-term averaged concentration within that sector is C=i,
[exp{
-eXp{
-(+>‘> -(z>“)]‘Ci.
N. J. DUIJM
1918
Wind dlrcrllon
4
300
200
100
0
0
Idegrees)
Fig. 2. Results for example 1, concentration vs wind direction measured at the sampling point, Squares: wind-tunnel data, line: l-h averaged concentrations using formula (8).
1
2
3
L
5
6
7
8 Wind
9
10
speed
11 12
13 IL
15 16 17 18
r 19 20
(m s-11
Fig. 3. Weibull distribution of wind speed in the Netherlands (Wieringa and Rijkoort, 1983). Scale factor 0=5.31, shape factor k=2.13.
The problem is how to define a general applicable relationship
between concentration
and wind speed. For sourceswithout any significant exit momentum or buoyancy, it may be assumed that concentration is
inversely proportional to wind speed: CT(“)=-& 1
al >o.
Wind-tunnel experiments at only one wind speed suffice to determine the constant (I~ for each wind direction sector. An unlimited number of wind speed
classescan then be defined, and using equation (10) the long-term averaged concentration can be determined at the required accuracy. It should be noted that the lowest wind speed at which concentration is (11) determined by this method should not be less than
Long-term
air quality
about 1 m s- ’ (at a height of 10 m). At lower wind speeds, dispersion is no longer dominated by wind speed generated turbulence (see e.g. Cagnetti and Ferrara, 1982). For sources with significant momentum and/or buoyancy, the concentration will attain a maximum at a certain wind speed: at low wind speeds, plumes will go over the sampling position, and at high wind speeds, the concentration will again become inversely proportional to wind speed. This behaviour depends on: buoyancy, momentum and exit direction of the source, and the position of the sampling point (at short distances from the source the concentration will attain its maximum at higher wind speeds than at larger distances). It is impracticable to perform detailed analysis of concentration as a function of wind speed for routine wind-tunnel measurements. To solve this problem, two strategies are discussed. The first, simplest strategy is to define a limited number of wind speed classes, each class to be represented by a representative wind speed. The “National Model” distinguishes 3 classes, namely O-2.5, 3-5.5 and above 6 m s-‘, with representative wind speeds of 1.454, and 8 m s- ‘. Using the wind speed distribution presented in Fig. 3 (a=5.31, k = 2.13) the frequency of occurrence is 22, 48 and 30%, respectively. The second strategy is to assume a functional behaviour of concentration which can be determined by a few (typically three) measurements. One function that obeys the boundary condition (low concentration at low wind speed, a maximum for medium wind speeds, and inversely proportional to high wind speeds) can be written as:
statistics
1919
Different stack heights were investigated and results for emissions 17.5 and 22.5 m above ground level are presented here. Source 2 consists of two vents ID 1.1 m and an exit velocity of 6 m s- ‘. Source 3 consists of only one vent ID 0.7 m and an exit velocity of 10 m s-i. The sample locations are indicated A (on the facade of the triangular “East” building) and B (on the roof of the “West” building). Concentration measurements were performed for a series of wind speed (at a height of 10m) ranging from 1 to 16 ms-‘. Using the second strategy, the curves in Fig. 5a-e are constructed. The presented curves are approximately the best fits, depending on the choice of the three data points used to determine the constants aI. a2 and a3. The best results are obviously obtained when the selected data points cover the low wind speed range, the maximum concentration, and the high wind speed range, respectively. It appears, however, that the lowest wind speed data point may be quite close to the maximum concentration, and the highest wind speed data point may be at quite high wind speeds to obtain good results, but the uncertainty is quite high. As the wind speed where the maximum concentration occurs is unknown beforehand for routine investigations, the effect of the data point selection on the accuracy was investigated. Table 1 shows an overview of results for example 2. The first column lists the averaged concentration calculated using all measurements and weighted with the Weibull distribution presented above, thus presenting the most accurate approximation. The second column lists the differences that will occur when the simple strategy with fixed wind speed classes is used. The third column lists the differences that will occur when the constants a,,a2.a3 in for1 mulae (12) are calculated by measurements at fixed C(U)= a,U+a,+a,JU wind speeds of 1.5,4, and 8 m s-i, followed by subdivision of wind speed in classes as presented in Fig. 3. with The last column shows the possible variation in resa$-4a,a3
N. J. DUIJM
1920 Building
‘West’
Central
Budding
+ 16n.
Fig. 4. Configuration
of example 2, dispersion of vent stack emissions from an industrial laboratory. 1, 2, and 3 are source locations, A and B are receptor locations.
of concentration as a function of wind speed quite well. The use of formula (12) is therefore only justified if the variation ofconcentration for intermediate wind speeds must be predicted. This may be the case if an hour by hour simulation of concentration has to be performed. DISCUSSION
The proposed methodology has been developed based on a wind direction resolution of S”, corresponding to the resolution used by the Dutch “National Model”. In order to reduce the experimental effort, it is tempting to reduce the wind-direction resolution of the wind-tunnel measurements. From Fig. 2 one may conclude that a resolution of lo” will yield a correct representation of the hourly averaged concentrations after the overlapping procedure, and a resolution of 15” can be considered at the cost of loss of accuracy of a few percent. As wind-tunnel concentration measurements near buildings can show steep gradients with wind direction, an u priori selection of wind-direction stepsize larger than IO” is not recommended. Another point of discussion is the applicability of formulae (12). As it presents a phenomenological description of concentration as a function of wind speed, it is believed to be applicable to both momentumdriven and buoyancy-driven emissions. It has already been stated that the measurements in
a neutrally stratified boundary layer wind tunnel can be used for the prediction of long-term air quality statistics even if the atmosphere is non-neutral for part of the time, as long as the lateral dispersion coefficients used for the overlapping technique account for the non-neutral atmospheric stabilities. However, as for Gaussian plume models. no attempt should be made to include predictions for wind speeds less than about 1 m s- ‘. The percentile method as presented is based on the use of a predefined probability density function. A number of methods based on the Gaussian plume model reconstruct the probability density by performing calculations for a long series of hours using actual meteorology. By use of formulae (12), the wind-tunnel technique presented herein can be used in the same way. When no attempt is made to predict concentrations paired in time, stability effects can probably be discarded for this application as well. When attempts are made to predict hourly averaged concentrations, stability effects are to be considered. Based on criteria for dense gas dispersion in the lee of a building, see Britter and McQuaid (1988), stability effects are probably negligible for stably stratified atmosphere if AT ,.g.H ‘a u2
< 10-2
Long-term
air quality
statistics
1921
0.010 0.009 0.009 0.00, 0.00, 0.001 0.004 0.00, 0.001 0.00, 0.000 9
6
Wind
IO
speed
11
I4
19
I9
10
Im 5.1)
0.001‘
o.ooa* o.ooaa 0.0010 ;; u z 5 .P z L zz
0.0011
2 u
0.0009
0.001‘ 0.0014 O.OO,l 0.0010
0.0009 0.0004 0.0001 0.0000
;
0
,
1
,
,
2
,
(
4
‘
Wind
,
,
,
(
9
speed
(
10
,
,
12
,
,
I4
(
,
I‘
,
,
I6
10
Im s.1)
0.0026 0.0024 0.0022 0.0010
Z ” \ ”
0.0016 0.0016 0.0014
.-z z b z 5 u
0.0012 0.0010 0.0006 0.0006 0.0004 0.0001 0.0000 0
4
6
6
Wind Fig.
speed
10
im s-1)
5. (a)-(c).
12
14
16
16
20
1922
N. J. DUIJM 0.0020 0.0019 0.0016 0.0017 0.0016
cd) . -
0.0016 0.0014 0.0013
-
0.0012 0.0011
-
0.0010 0.0009 0.0006 0.0007 0.0006 0.0006 0.0004 0.0003 0.0002 0.0001 0.0000
-
-
0 1 0
I 2
I
I *
I
I 6
I
Wind
I 6
!
speed
I 10
I
I 12
11
I 14
I 16
I1
1 16
20
Im s-1)
S 0.0007 Y $-I 0.000‘ .-I 0.0003 zL 2 0.0004 :: z 0.0003 0.0002 0.0001
f , , , , , , I , , , , , , , , , , , , 0.0000 0 2 4 6 8 IO I? 1. 16 16 10 Wind
speed
h
s 11
Fig. 5. Results for example 2. concentration as a function of wind speed; (a) source 1 at 17.5 m above ground and receptor B at 85 wind direction;(b) source 1 at 22.5 m above ground and receptor B at 85 wind direction;(c) source 1 at 22.5 m above ground and receptor A at 265. wind direction; (d) source 2 and receptor A at 300~ wind direction: and (e) source 3 and receptor A at 300’ wind direction.
where T, is ambient temperature (K); AT is temperature difference between ground and building height H, g is gravitational acceleration and U is wind speed at building height H.
CONCLUSION
A method is proposed which enables the calculation of the frequency distribution of pollutant concentrations from routine wind tunnel investigations which is compatible with the Dutch “National
Model”. The method requires wind tunnel measurements for every 5 of wind direction change, and at three wind speeds if momentum or buoyancy from the source cannot be ignored. The wind-tunnel measurements are corrected for lack of horizontal meandering in the wind tunnel by a numerical overlapping technique in order to obtain l-h averaged concentrations. The effect of wind speed can be included by defining at least three wind speed classes which approximate the wind speed distribution. A simple formula enables the
description
of the
variation
of concentration
with
wind speed, but the results are quite sensitive to the
Long-term Table
Example
I. Long-term
averaged
Best approximation
C/C,(%)
4.35 1.27 0.58 0.89 0.52
2a
2b 2c 2d
2e
air quality
concentrations
calculated
two
different
Calculated using formula (12) and three fixed data points*
(difference with best approximation)
(difference with best approximation)
-2% +6% +9% -26% -4%
selection of the three wind speeds needed to determine the empirical parameters, and there is little advantage compared to the assumption that concentration does not vary within one wind speed class.
REFERENCES Britter R. E. and McQuaid J. (1988) Workbook on the dispersion of dense gases. HSE contract research report No. 17/1988, Health and Safety Executive, Sheffield, U.K. Builtjes P. J. H. (1982) Turbulent dilfusivities and dispersion coefficients: application to calm wind conditions. Sci. total Enuir. 23, 107-I 18. Cagnetti P. and Ferrara V. (1982) Two possible simplified diffusion models for very low wind-speed. Rivista di aeronaurica
using
Calculated using three fixed wind speed classes*
*The fixed wind speed classes or data points are 1.54 obtained by extrapolation if no data were measured.
mereorologica
1923
statistics
42, 399403.
Commissie Onderzoek Luchtverontreiniging (1976) Models for the calculation of the dispersion of air pollution. including recommendations for the values of parameters in the long-term model. Study and Information Centre TN0 for Environmental Research, P.O. Box 186, 2600 AD Delft. The Netherlands.
techniques
(see text)
Calculated using formula (12) and all possible combinations of data points (max.
0% +l5%
+ 12% +19% -2% and 8 m s -I. The concentration
difference with best approximation)
- 13%/+ 13% -30%/+28% - 15%/+23% -28%/+26% - 19%/+36% data at I.5 ms-’
are
Commissie Onderzoek Luchtverontreiniging (1981) Frequency distributions of air pollution concentrations; recommendations for a method of calculation. Study and Information Centre TN0 for Environmental Research, P.O. Box 186, 2600 AD Delft. The Netherlands. Commissie Onderzoek Luchtverontreiniging (1984) Parameters in the long-term model of air pollution disper-
sion-new
recommendations.
Study and Information
Centre TN0 for Environmental Research, P.O. Box 186, 2600 AD Delft, The Netherlands. Guldemond C. P. and Bakker C. (1986) Evaluation of the Dutch national dispersion model with selected measurements of specific components. Paper presented at the 7th World Clean Air Congress, Sydney, Australia, 25-29 August 1986. Ide Y., Ohba R. and Okabayashi K. (1991) Development of overlapping modelling for atmospheric diffusion. Mitsubishi technical bulletin No. 194, Mitsubishi Heavy Industries Ltd. 5-l. Marunouchi 2-chome, Chiyoda-ku, Tokyo. Japan. Wieringa J. and Rijkoort P. J. (1983) Windklimaat van Nederland (in Dutch). KNMI, De Bilt, Staatsuitgeverij The Hague, The Netherlands.
Armo\phcrir Enwronmenr Vol. 28. No. I I. Pp. 191>1923. 1994 Elsewcr Science Ltd Printed in Great Britain. 1352-2310194 f7.00+0.00
LONG-TERM
AIR QUALITY WIND-TUNNEL
STATISTICS DERIVED INVESTIGATIONS
N. J. TNO-Institute
for
Environmental
and
DUIJM
Energy Technology The Netherlands
(IMET),
P.O.
Abstract-Wind-tunnel investigations are commonly used to determine vicinity of buildings. Results of these investigations should be comparable used to express air quality standards. An analysis method for wind-tunnel data is proposed which enables distribution of pollutant concentrations which is compatible with the outcome IS long-term averaged concentrations as well as percentile values trations. The method takes into account the lack of horizontal meandering the real atmosphere and the effect of wind speed. Key
lord
it1de.c
Averaged
concentration,
frequency
distribution,
INTRODUCTION
Netherlands air quality standards are expressed as yearly averaged values and “percentile values”. The standard for e.g. NO2 is 9%percentile 135 pg me3, 99.5 percentile 175 pg rnm3, based on hourly mean values (i.e. 135 pgrnm3 should not be exceeded in 2% of the hours per year, 175 p’grnm3 should not be exceeded in 0.5% of the hours per year). In general. air pollutant levels are a result of background pollution levels, i.e. due to sources in the wide surroundings, and of local pollution sources. In order to decide whether the contribution of additional local sources is acceptable in terms of air quality. predictions
need
to
be made.
wind-tunnel
This
paper
measurements deals
wind-tunnel
data
information
on
tional
Model”
with
the
should analysis
necessary air
quality
to
obtain
consistent
be used.
requirements the with
of
required the
Box
342. 7300 AH
pollutant concentrations in the and compatible with the format the calculation of the frequency Dutch “National Model”. The based on I-h averaged concenin the wind tunnel compared lo
percentiles,
wind
“Na-
guidelines.
OUTLINE
OF THE
“NATIONAL
speed,
building
effects.
Predictions of the LTA concentrations are made using the “narrow plume” assumption, i.e. assuming that plumes are within a sector of 30” and that the wind direction probability within each sector of 30” is uniform. The basic Gaussian plume formula for the LTA concentration at ground level (x, y) from a source at origin (0. 0, H) is:
exp[- H*/(2&)1
(1)
where
The recommendations SHORT
Apeldoorn,
S is the stability class N is the wind speed class Q is the yearly averaged source strength (kgs-‘) .f is the probability of wind direction 0 (when point (I. ~1)is downwind of the source), stability S and wind speed class N Us is the representative wind speed for class N(m s-‘) cr,S is the vertical dispersion coefficient for stability class S, (~,.s is an empirical function of downwind distance x(m) II is the number of wind direction sector (for 30 sector, n= 12) I downwind distance from source (m) H plume height (m).
For free-standing stacks on flat terrain, predictions can be made using Gaussian plume models. In the Netherlands. a recommended guideline. generally known as the “National Model” is used to predict the contribution of local sources to yearly averaged concentrations and percentile values in simple situations. Although the “National Model”. includes a guideline for dispersion calculations around a cubic building. for reliable air quality predictions in built-up environments
FROM
l
MODEL”
l
GUIDELINES
include:
description of stability and the empirical functions of coefficient 0,; models to calculate H from long-term statistics of j(0, meteorological stations.
wind speed classes; the vertical dispersion
The “National Model” guidelines (Commissie Onderzoek Luchtverontreiniging. hereafter named COL, 1976, 1981, 1984) describe the prediction of:
l
l long-term 0 percentile
The section of the “National Model” dealing with the prediction of percentile values is generally known
averaged (LTA) values.
l
concentrations 1915
AE 28:11-H
plume rise; S, N) for two Dutch
1916
N. J. DUIJM
as the “long-term frequency distribution” (LTFD) model (COL, 1981; Guldemond*and Bakker, 1986). The LTFD model calculates frequency distributions of 1 h averaged concentrations based on LTA values in wind direction sectors of 5 degrees and on the frequency of occurrence of the wind direction corresponding to each of those sectors. Assuming a two-parameter log-normal distribution in each sector, the frequency at which a defined concentration is exceeded in a sector can be calculated from the sector averaged value and the geometric standard deviation (GSD, the standard deviation of the frequency distribution of log(concentration)), of the concentration distribution in that sector. For reasons of simplicity, the model assumes that the GSD is the same for every sector. Taking into account the frequency of occurrence of every wind direction, the overall frequency at which the defined concentration is exceeded can be calculated. The concentration that will be exceeded in a defined period of time, e.g. 5% (the 95-percentile), can then be computed through an iteration procedure. In the model a value for the GSD of 0.7 is suggested for chemically inert components; this value was found to be applicable in test runs with SOz (COL, 1981). The generality of this value might be doubted (Guldemond and Bakker, 1986). In order to transform the LTA concentrations (based on 30” sectors) to the 5” sector, the lateral dispersion coefficient uys is used. Empirical values for gys as a function of x are recommended. These dispersion coefficients describe hourly averaged plumes. The correct use of the LTFD model is (a) to determine the yearly averaged concentration wind rose of background concentration (at 5” sectors) from routine air quality measurements; (b) to calculate the required percentile value of the background concentrations using the LTFD model; (c) to add the concentration wind rose from the new source under consideration to the background; and (d) to calculate the percentile value of the total concentrations. The difference between the results of steps (d) and (b) is the increase in the percentile value.
If, for example, hourly averaged plumes need to be simulated, additional meandering or wind direction fluctuations that occur on time scales between the averaging time corresponding to the wind tunnel simulation and the required averaging times (e.g. 1 h) can be described by a Gaussian probability density distribution with standard deviation ee P(v)=-
1‘p2 1 I ---
J&ueexp
Here, ‘p is the deviation of wind direction from the hourly mean wind direction. The hourly mean concentration at location (x, y) can be constructed for a flat terrain from the windtunnel data by m Chow k Y) =
GvT(x. y-cp.-u).p(cp)dv.
MEAN
CONCENTRATIONS
WIND-TUNNEL
DERIVED
-m
ev
(4)
Here, U is the mean convection velocity of the plume, and/(z) describes the vertical distribution of the concentration. The solution of this convolution integral is
-! i
FROM
” 2 a;wr+xza;
I (5)
MEASUREMENTS
The width of a plume over flat terrain can be described by the dispersion coefficient cry. The dispersion coefficient is not only a function of distance and atmospheric stability but also of averaging time (see e.g. Builtjes, 1982). When similar plumes are measured in wind tunnels, plume width is normally independent of averaging time. This means that wind-tunnel simulations only represent plumes of a certain averaging time, depending on the scale factor and wind-tunnel characteristics. For most wind-tunnel simulations, this will be of the order of a few minutes.
(3)
If Cwr(x, y) can be described in terms of a Gaussian plume with lateral dispersion coefficient eYwT, this can be written as:
x.f(z) .exp HOURLY
(2)
2.6
From this, it follows ueJz=+ x
(6)
cry, the full-scale hourly averaged dispersion coefficient, can be derived from empirical data or recommended values (COL, 1977, 1981, 1984). uYwT is to be measured from dispersion experiments in a wind tunnel with an undisturbed boundary layer. Instead of uY. direct measurement of wind direction variations at full scale can be used. For wind-tunnel values direct measurement of uywT from dispersion
1917
Long-term air quality statistics experiments is recommended for better accuracy and reliability. The information obtained can now be used for the correction of wind tunnel measurements of dispersion affected by obstacles. A “wind rose” of concentration should therefore be measured. The resolution of measurements should be of the order of 5”. Those measurements can than be corrected according to
canopy + L 5 m ---
-----
1
+ J-n:
which is approximated
by
--.
! I
ChO"A@)=
f: i=-n
-
I
JiYUe
T
sample point 14 I
xexp{-p$}
x Cwr(O + i Aq).
/
c!/3
t
1.5 m.
(8)
'
I
’
I/a 'I
Here, Acp is the wind direction difference between subsequent wind-tunnel measurements. This method can be called “overlapping modelling by calculation”, see e.g. Ide er al. (1991).
Evample 1 The methodology described above is illustrated by measurements of the dispersion of hydrocarbons due to the filling of fuel tanks at petrol stations. The configuration is shown in Fig. 1, the canopy is at a height of 4.5 m. The sampling points are at a height of 1.5 m; sampling point 14 is at the edge of the canopy. Wind-tunnel tests at scale 1 to 100 were carried out at TNO-IMET’s wind tunnel No. 2. The roughness length z,, of the boundary layer was 2 x 10m4 m, the wind speed at 100 mm was 8 ms-‘. The source emission was 6.4 x 10m6 m3 s-’ with 2% tracer gas (isobutylene). Figure 2 shows the measured concentration at the sampling point as a function of wind direction. The correction for meandering is also shown. For this case cB is 52, derived from measurements of plume width in the wind tunnel at 1540 mm (152 mm) and recommended values of uY for neutral stability c7Y= 0.470 .P90’ . zy As could be expected, inclusion of meandering leads to lower peak concentrations and wider plumes. In this case, the recommended value of CT~for neutral stability was used. At sufficiently high wind speed dispersion around buildings will be dominated by mechanically induced turbulence, which justifies the use of neutrally stratified boundary layer wind tunnels for the prediction of long-term averaged concentrations near obstacles. However, large-scale meandering depends on stability and lateral dispersion coefficients for all stabilities should therefore be used, weighted with the
Fig. I. Configuration of example 1, dispersion of benzene at a petrol station. relative frequency of occurrence in question. THE
EFFECT
OF WIND
for the wind direction
SPEED
AND
WIND
SPEED
STATISTICS
Concentrations depend on wind speed. The longterm averaged concentration therefore also depends on the wind speed statistics. Wind speed statistics in the Netherlands can be reasonably well described by a Weibull distribution: (Wieringa and Rijkoort, 1983) p(U>U,)=exp
{
$ (
k >I
(9)
Here, a is known as the scale factor, and k is known as the shape factor (Fig. 3). If within a wind direction sector, wind speed classes i are defined by lower limit Ui-l and upper limit Vi and the concentration Ci for every class is also known, the long-term averaged concentration within that sector is C=i,
[exp{
-eXp{
-(+>‘> -(z>“)]‘Ci.
N. J. DUIJM
1918
Wind dlrcrllon
4
300
200
100
0
0
Idegrees)
Fig. 2. Results for example 1, concentration vs wind direction measured at the sampling point, Squares: wind-tunnel data, line: l-h averaged concentrations using formula (8).
1
2
3
L
5
6
7
8 Wind
9
10
speed
11 12
13 IL
15 16 17 18
r 19 20
(m s-11
Fig. 3. Weibull distribution of wind speed in the Netherlands (Wieringa and Rijkoort, 1983). Scale factor 0=5.31, shape factor k=2.13.
The problem is how to define a general applicable relationship
between concentration
and wind speed. For sourceswithout any significant exit momentum or buoyancy, it may be assumed that concentration is
inversely proportional to wind speed: CT(“)=-& 1
al >o.
Wind-tunnel experiments at only one wind speed suffice to determine the constant (I~ for each wind direction sector. An unlimited number of wind speed
classescan then be defined, and using equation (10) the long-term averaged concentration can be determined at the required accuracy. It should be noted that the lowest wind speed at which concentration is (11) determined by this method should not be less than
Long-term
air quality
about 1 m s- ’ (at a height of 10 m). At lower wind speeds, dispersion is no longer dominated by wind speed generated turbulence (see e.g. Cagnetti and Ferrara, 1982). For sources with significant momentum and/or buoyancy, the concentration will attain a maximum at a certain wind speed: at low wind speeds, plumes will go over the sampling position, and at high wind speeds, the concentration will again become inversely proportional to wind speed. This behaviour depends on: buoyancy, momentum and exit direction of the source, and the position of the sampling point (at short distances from the source the concentration will attain its maximum at higher wind speeds than at larger distances). It is impracticable to perform detailed analysis of concentration as a function of wind speed for routine wind-tunnel measurements. To solve this problem, two strategies are discussed. The first, simplest strategy is to define a limited number of wind speed classes, each class to be represented by a representative wind speed. The “National Model” distinguishes 3 classes, namely O-2.5, 3-5.5 and above 6 m s-‘, with representative wind speeds of 1.454, and 8 m s- ‘. Using the wind speed distribution presented in Fig. 3 (a=5.31, k = 2.13) the frequency of occurrence is 22, 48 and 30%, respectively. The second strategy is to assume a functional behaviour of concentration which can be determined by a few (typically three) measurements. One function that obeys the boundary condition (low concentration at low wind speed, a maximum for medium wind speeds, and inversely proportional to high wind speeds) can be written as:
statistics
1919
Different stack heights were investigated and results for emissions 17.5 and 22.5 m above ground level are presented here. Source 2 consists of two vents ID 1.1 m and an exit velocity of 6 m s- ‘. Source 3 consists of only one vent ID 0.7 m and an exit velocity of 10 m s-i. The sample locations are indicated A (on the facade of the triangular “East” building) and B (on the roof of the “West” building). Concentration measurements were performed for a series of wind speed (at a height of 10m) ranging from 1 to 16 ms-‘. Using the second strategy, the curves in Fig. 5a-e are constructed. The presented curves are approximately the best fits, depending on the choice of the three data points used to determine the constants aI. a2 and a3. The best results are obviously obtained when the selected data points cover the low wind speed range, the maximum concentration, and the high wind speed range, respectively. It appears, however, that the lowest wind speed data point may be quite close to the maximum concentration, and the highest wind speed data point may be at quite high wind speeds to obtain good results, but the uncertainty is quite high. As the wind speed where the maximum concentration occurs is unknown beforehand for routine investigations, the effect of the data point selection on the accuracy was investigated. Table 1 shows an overview of results for example 2. The first column lists the averaged concentration calculated using all measurements and weighted with the Weibull distribution presented above, thus presenting the most accurate approximation. The second column lists the differences that will occur when the simple strategy with fixed wind speed classes is used. The third column lists the differences that will occur when the constants a,,a2.a3 in for1 mulae (12) are calculated by measurements at fixed C(U)= a,U+a,+a,JU wind speeds of 1.5,4, and 8 m s-i, followed by subdivision of wind speed in classes as presented in Fig. 3. with The last column shows the possible variation in resa$-4a,a3
N. J. DUIJM
1920 Building
‘West’
Central
Budding
+ 16n.
Fig. 4. Configuration
of example 2, dispersion of vent stack emissions from an industrial laboratory. 1, 2, and 3 are source locations, A and B are receptor locations.
of concentration as a function of wind speed quite well. The use of formula (12) is therefore only justified if the variation ofconcentration for intermediate wind speeds must be predicted. This may be the case if an hour by hour simulation of concentration has to be performed. DISCUSSION
The proposed methodology has been developed based on a wind direction resolution of S”, corresponding to the resolution used by the Dutch “National Model”. In order to reduce the experimental effort, it is tempting to reduce the wind-direction resolution of the wind-tunnel measurements. From Fig. 2 one may conclude that a resolution of lo” will yield a correct representation of the hourly averaged concentrations after the overlapping procedure, and a resolution of 15” can be considered at the cost of loss of accuracy of a few percent. As wind-tunnel concentration measurements near buildings can show steep gradients with wind direction, an u priori selection of wind-direction stepsize larger than IO” is not recommended. Another point of discussion is the applicability of formulae (12). As it presents a phenomenological description of concentration as a function of wind speed, it is believed to be applicable to both momentumdriven and buoyancy-driven emissions. It has already been stated that the measurements in
a neutrally stratified boundary layer wind tunnel can be used for the prediction of long-term air quality statistics even if the atmosphere is non-neutral for part of the time, as long as the lateral dispersion coefficients used for the overlapping technique account for the non-neutral atmospheric stabilities. However, as for Gaussian plume models. no attempt should be made to include predictions for wind speeds less than about 1 m s- ‘. The percentile method as presented is based on the use of a predefined probability density function. A number of methods based on the Gaussian plume model reconstruct the probability density by performing calculations for a long series of hours using actual meteorology. By use of formulae (12), the wind-tunnel technique presented herein can be used in the same way. When no attempt is made to predict concentrations paired in time, stability effects can probably be discarded for this application as well. When attempts are made to predict hourly averaged concentrations, stability effects are to be considered. Based on criteria for dense gas dispersion in the lee of a building, see Britter and McQuaid (1988), stability effects are probably negligible for stably stratified atmosphere if AT ,.g.H ‘a u2
< 10-2
Long-term
air quality
statistics
1921
0.010 0.009 0.009 0.00, 0.00, 0.001 0.004 0.00, 0.001 0.00, 0.000 9
6
Wind
IO
speed
11
I4
19
I9
10
Im 5.1)
0.001‘
o.ooa* o.ooaa 0.0010 ;; u z 5 .P z L zz
0.0011
2 u
0.0009
0.001‘ 0.0014 O.OO,l 0.0010
0.0009 0.0004 0.0001 0.0000
;
0
,
1
,
,
2
,
(
4
‘
Wind
,
,
,
(
9
speed
(
10
,
,
12
,
,
I4
(
,
I‘
,
,
I6
10
Im s.1)
0.0026 0.0024 0.0022 0.0010
Z ” \ ”
0.0016 0.0016 0.0014
.-z z b z 5 u
0.0012 0.0010 0.0006 0.0006 0.0004 0.0001 0.0000 0
4
6
6
Wind Fig.
speed
10
im s-1)
5. (a)-(c).
12
14
16
16
20
1922
N. J. DUIJM 0.0020 0.0019 0.0016 0.0017 0.0016
cd) . -
0.0016 0.0014 0.0013
-
0.0012 0.0011
-
0.0010 0.0009 0.0006 0.0007 0.0006 0.0006 0.0004 0.0003 0.0002 0.0001 0.0000
-
-
0 1 0
I 2
I
I *
I
I 6
I
Wind
I 6
!
speed
I 10
I
I 12
11
I 14
I 16
I1
1 16
20
Im s-1)
S 0.0007 Y $-I 0.000‘ .-I 0.0003 zL 2 0.0004 :: z 0.0003 0.0002 0.0001
f , , , , , , I , , , , , , , , , , , , 0.0000 0 2 4 6 8 IO I? 1. 16 16 10 Wind
speed
h
s 11
Fig. 5. Results for example 2. concentration as a function of wind speed; (a) source 1 at 17.5 m above ground and receptor B at 85 wind direction;(b) source 1 at 22.5 m above ground and receptor B at 85 wind direction;(c) source 1 at 22.5 m above ground and receptor A at 265. wind direction; (d) source 2 and receptor A at 300~ wind direction: and (e) source 3 and receptor A at 300’ wind direction.
where T, is ambient temperature (K); AT is temperature difference between ground and building height H, g is gravitational acceleration and U is wind speed at building height H.
CONCLUSION
A method is proposed which enables the calculation of the frequency distribution of pollutant concentrations from routine wind tunnel investigations which is compatible with the Dutch “National
Model”. The method requires wind tunnel measurements for every 5 of wind direction change, and at three wind speeds if momentum or buoyancy from the source cannot be ignored. The wind-tunnel measurements are corrected for lack of horizontal meandering in the wind tunnel by a numerical overlapping technique in order to obtain l-h averaged concentrations. The effect of wind speed can be included by defining at least three wind speed classes which approximate the wind speed distribution. A simple formula enables the
description
of the
variation
of concentration
with
wind speed, but the results are quite sensitive to the
Long-term Table
Example
I. Long-term
averaged
Best approximation
C/C,(%)
4.35 1.27 0.58 0.89 0.52
2a
2b 2c 2d
2e
air quality
concentrations
calculated
two
different
Calculated using formula (12) and three fixed data points*
(difference with best approximation)
(difference with best approximation)
-2% +6% +9% -26% -4%
selection of the three wind speeds needed to determine the empirical parameters, and there is little advantage compared to the assumption that concentration does not vary within one wind speed class.
REFERENCES Britter R. E. and McQuaid J. (1988) Workbook on the dispersion of dense gases. HSE contract research report No. 17/1988, Health and Safety Executive, Sheffield, U.K. Builtjes P. J. H. (1982) Turbulent dilfusivities and dispersion coefficients: application to calm wind conditions. Sci. total Enuir. 23, 107-I 18. Cagnetti P. and Ferrara V. (1982) Two possible simplified diffusion models for very low wind-speed. Rivista di aeronaurica
using
Calculated using three fixed wind speed classes*
*The fixed wind speed classes or data points are 1.54 obtained by extrapolation if no data were measured.
mereorologica
1923
statistics
42, 399403.
Commissie Onderzoek Luchtverontreiniging (1976) Models for the calculation of the dispersion of air pollution. including recommendations for the values of parameters in the long-term model. Study and Information Centre TN0 for Environmental Research, P.O. Box 186, 2600 AD Delft. The Netherlands.
techniques
(see text)
Calculated using formula (12) and all possible combinations of data points (max.
0% +l5%
+ 12% +19% -2% and 8 m s -I. The concentration
difference with best approximation)
- 13%/+ 13% -30%/+28% - 15%/+23% -28%/+26% - 19%/+36% data at I.5 ms-’
are
Commissie Onderzoek Luchtverontreiniging (1981) Frequency distributions of air pollution concentrations; recommendations for a method of calculation. Study and Information Centre TN0 for Environmental Research, P.O. Box 186, 2600 AD Delft. The Netherlands. Commissie Onderzoek Luchtverontreiniging (1984) Parameters in the long-term model of air pollution disper-
sion-new
recommendations.
Study and Information
Centre TN0 for Environmental Research, P.O. Box 186, 2600 AD Delft, The Netherlands. Guldemond C. P. and Bakker C. (1986) Evaluation of the Dutch national dispersion model with selected measurements of specific components. Paper presented at the 7th World Clean Air Congress, Sydney, Australia, 25-29 August 1986. Ide Y., Ohba R. and Okabayashi K. (1991) Development of overlapping modelling for atmospheric diffusion. Mitsubishi technical bulletin No. 194, Mitsubishi Heavy Industries Ltd. 5-l. Marunouchi 2-chome, Chiyoda-ku, Tokyo. Japan. Wieringa J. and Rijkoort P. J. (1983) Windklimaat van Nederland (in Dutch). KNMI, De Bilt, Staatsuitgeverij The Hague, The Netherlands.