- Email: [email protected]
Field experiments of dispersion through regular arrays of cubic structures
Pergamon
Annospheru.
PII: S1352-2310(96)00263-4
Environment Vol. 31, No. 6, pp. 783-795, 1997 Copyright s$’ 1996 Elsevier Swnce Ltd Printed in Great Britam All rights reserved 1352-2310’97 $1700 + 0.00
FIELD EXPERIMENTS OF DISPERSION THROUGH REGULAR ARRAYS OF CUBIC STRUCTURES and R. F. GRIFFITHS
R. W. MACDONALD
Environmental Technology Centre, UMIST, P.O. Box 88, Manchester M60 lQD, U.K.
and S. C. CHEAH Ministry of Defence, PLSD, Porton Down, Salisbury SP4 OJQ, U.K. (First received 10 April 1996 and in final
form
25 August 1996)
Abstract-To investigate the effect of plan area density on the near-field dispersion of pollutant plumes in built-up areas, scaled field measurements have been made of the dispersion of a plume released upwind of regular arrays of cubes of varying plan area density. It was found that the lateral concentration profiles were Gaussian in all cases. Close to the source, the lateral dispersion parameter oYwas increased, relative to that of a plume in open terrain and was highest for the most dense array. Despite the increased plume dimensions in the array, the reduction in advection velocity resulted in ground-level concentrations that were in general not too different from those of a plume in open terrain. This behaviour can be modelled by a Gaussian-plume-type expression for time-averaged concentration. Copyright c 1996 Elsevier Science Ltd Ke)) word index: Atmospheric diffusion, urban pollution, building effects, Gaussian plume. atmospheric boundary layer.
1. INTRODUCTION
Most studies of urban dispersion in the past have been concerned either with long-range urban dispersion, where the plume dimensions are much larger than the individual buildings, or short-range diffusion around single or small groups of buildings. Excellent reviews on the latter subject exist (Hosker, 1984; Meroney, 1982) and various working models can be found for longer-range urban diffusion (Hanna et al., 1982). It is only relatively recently that the short-range dispersion problem in urban environments has been systematically studied. This is a surprising state of affairs, given that the greatest potential for damage to human health occurs in the near-field of toxic releases in an urban environment. In a recent study of urban dispersion from point sources, Davidson et al. (1995) identified several important characteristics of near-field plume behaviour for point sources in a relatively sparse array of buildings (ratio of gap between buildings to building height S/H = 2). The importance of the relative size of the plume to the obstacle array was indicated and within this type of array, it was found that the lateral plume concentration profile remained Gaussian, while a reflected Gaussian was a plausible fit for the vertical distribution. The plume CJ,,Swere similar to those of a control plume, but the vertical growth was enhanced
within the array. The mean concentrations were also comparable to a control plume, a result shown to be consistent with a reduction of mean velocity within the array. Theurer (1995) and Baechlin et al. (1992) found that for more irregular arrays of buildings with aspect ratios greater than one, the near-field profiles were usually not Gaussian shaped, but were dominated by local building effects which sometimes caused a lateral shift of the plume. However, in the far field beyond the “radius of homogenisation”, the time-averaged behaviour of the plume was no longer affected by single obstacles, but was influenced globally by an effective roughness length zo. In this region a Gaussian plume model (GPM) again provided a good representation of the behaviour. Undoubtedly, a key factor in determining the nearfield plume dispersion behaviour is the plan area density of the buildings. It is well established that there are three different aerodynamic flow regimes which occur in arrays, depending on the building density. In regular arrays of cubic elements, the plan area density A,, is related to the gap between cubes S and their height H by 1 Aa’= (1 + LY/H)~’ 783
784
R. W. MACDONALD
Based on flow over separated and Lee,
the plan area density, proximity effects and arrays of cubic roughness, elements can be into three regimes (Morris, 1955; Hussain 1980):
(i) The isolated roughness flow regime occurs when A,, < 8-10% (S/H > 2.2-2.6). In this regime, the elements are sufficiently far apart that their flow separation bubbles reattach before the next element is reached. (ii) The wake interference flow regime occurs for element spacing values 9% < 1,, < 17% (1.2 < S/H < 2.4). In this case, the separation region behind each element does not have sufficient room to develop fully. (iii) The skimming flow regime exists for values of i,, > 15S21% (S/H < 1.2-1.6). Stable vortices are created behind the elements and the flow appears to skim on the crests of the elements. According to Turner (1973) many housing estates fall into the density range I,, = ll-20% (S/H = 1.2-2.0). Industrial estates are usually less dense. Therefore, in modelling urban dispersion it is necessary to look at all three flow regimes. Whereas Davidson et al. (1995) investigated an array with plan area density I,, = 11.1% in the wake interference regime, the current study extends this database to include arrays in all three aerodynamic flow regimes.
et al. 2. EXPERIMENTAL
2.1.
DETAILS
Field site und building models
The experiments were conducted at the UMIST Environmental Technology test site in Lancashire, Northwest England, where there are regular winds from the sea which is 2 km to the west of the test site. The surrounding terrain consists of light scrub brush and grass, which was kept mown to a height of a few centimetres for a distance of about 50 m upwind of the cube arrays. The surface roughness length z, was determined from wind measurements at the site and showed some dependence on the mean wind direction. For the predominant wind direction which was from the west to northwest, z, varied from about 5 to 25 mm. The building models were nominal cubes made of galvanised steel and were selected to represent a 1: 10 scale mode1 of a building of nominal height 10 m. Depending on the lay-out, up to 100 were used in the experiments. The face of the cubes was 1.15 m high and 1.10 m wide, giving a representative scale H = 1.125 m (so that HZ equals the frontal area of the cube). The arrays were set up in regular grid-iron arrangements in three array spacings: S/H = 0.5, 1.5 and 3.0 (Fig. 1). 2.2. Measurement apparatus A gas tracer of pure-grade propylene (C,H,) was released at a controlled flow rate from an open-ended hose 12 mm in diameter. The gas flow rate was measured using a float-type variable area rotameter. The low release flow rates employed in the experiments ensured that the gas was quickly diluted and that the passive diffusion phase of the tracer started near the source.
?? ?? ?? ?? ?? ?? ACI
:
:
:
:
mmmmmm i’ ;.i.i.;.m
6’ :
d
9’ :D b S/H=05
i.i.i.C.;.m i.i.L’i.C.m
??
??
??
??
??
??
i.i.i.i.;.m m ?? b+m
?? m
?? ?? ?? ?? ?? ?? a
s/H=15
Fig. 1. Geometry of the cube arrays studied with layout of UVICs indicated for the array with S/H = 1.5. (a) 8 x 8 array with S/H = 1.5; (b) detail of 10 x 10 array with S/H = 0.5; (c) detail of 7 x 7 array with S/H = 3.0 ( + : typical locations of anemometer to measure velocity behind cubes and gaps within the array).
Dispersion through regular arrays of cubic structures The propylene concentrations were measured with UVIC” (Ultra Violet Ion Collector) detectors of the research variety, made by Industrial Development Bangor (IDB) Limited. The UVICs detector is a type of photoionisation detector (PID) which has sensitivity down to 0.01 ppm by volume with a response time of about 0.02 s. A detailed description of this instrument and the calibration procedure is provided in Higson et al. (1995). Signals from the gas detectors were transmitted to the data acquisition computer using an FM telemetry system operating in the range 433.5-434.7 MHz. An A/D data acquisition system mounted in the microcomputer was used to convert the signals to discrete voltage data at a sampling frequency of 50 Hz. Upwind mean and fluctuating velocity components were measured by Gill Research ultrasonic anemometers positioned 6-10 H upwind of the various arrays at a height of 1H above the ground. The sonic anemometer sampled the three orthogonal components of velocity at a frequency of 21 Hz, with a response time of 0.1 s. The anemometer also provided instantaneous temperature readings which allowed the calculation of heat flux. A variety of software was written to calculate the mean velocity U,,, the mean wind direction 0, the standard deviation of horizontal wind direction bg, the standard deviation of vertical wind direction cm, the Monin-Obukhov length scale L, and the surface roughness parameter za, all evaluated at height H. 2.3. Experimental
procedure
and selection
of averaging time
The basic experiment involved laying out UVIC@ detectors behind each row of the array to monitor the lateral distribution of concentration as well as the change of concentration with depth in the array. A maximum of 10 instruments at a time were used in each row. The UVIC” detectors and source were set at a height of H/2, with the source a distance 2H upwind of the array. The detectors were located at a distance H/2 behind the cubes in each row except in the most dense array, where they were H/4 behind the cubes. Figure 1 shows the position of the source and detectors set up in the 8 x 8 array with spacing S/H = 1.5, along with details of the other two array geometries studied. The x-axis is aligned with the mean wind direction and is measured from the source position. Gas was released and sampled continuously for 15 min in each experiment. From each record of wind direction, the three-minute period with the least variation of mean wind was selected as the standard sampling period for all mean concentrations and mean wind speed values quoted below. There are several reasons for choosing a three-minute averaging time: (i) Three minutes is the longest period that the mean wind stayed in an effectively constant direction in all the experiments. (ii) The purpose of the experiments was to look at the effect of the arrays on the diffusion. Since the scale of the turbulence generated within the array is of order H/U (typically about 0.2 s), such a time scale is well averaged over three minutes. (iii) If one averages over longer periods such as 15-20 min, the random passage of large-scale eddies due to phenomena other than the boundary-layer generation of turbulence leads to slow variations in wind direction. The resulting lateral meandering of the plume tends to overwhelm the time-averaged diffusion induced by the cubes; so that the contribution of the array to by would not be discernible. (iv) The effect of averaging time on concentration has been examined and concentrations for averaging times between 10 s and 15 min. tend to follow a simple power law, equation (5). The measured concentrations were non-dimensionalised as follows: K, = 10-6CU,HZ/Q
(2)
785
where C is mean concentration in ppm, Q is source strength in m3 s- ’Ui, is the upwind velocity at cube height in m s- ’ and H is in m. The measurement uncertainty in the calculated value of K, was estimated to be about 16%.
3. RESULTS AND DISCUSSION 3.1. Turbulence
characteristics
upwind
of the array
Davidson et al. (1995) reported that plume statistics from their field and wind tunnel studies could be made to collapse onto non-dimensional curves using length scales of the upstream turbulence. Measurements of the integral length scales of the upstream turbulence were also made at the present test site and the results were found to be very sensitive to the sampling time used. The measured integral length scales are shown in Table 1 for the longitudinal direction (I,,), lateral direction (I,,) and vertical direction (L,). These were calculated from the autocorrelation function as discussed in Davidson et al. (1995). The longitudinal and lateral length scales vary by a factor of lo-20 depending on the averaging block times shown. The vertical length scale is relatively insensitive to the detrending process because this length scale is limited by the presence of the ground and there are no slow time variations in the vertical direction as there are in the horizontal directions. Given that the integral length scales calculated from fixed-point wind data are so strongly sensitive to the detrending procedures used, dispersion data in this paper were non-dimensionalised with the obstacle Hz instead of using turbulence length dimension scales. It would be inappropriate to use the integral length scales in the non-dimensionalisation since they are so variable, being dependent upon averaging time. Since the horizontal and vertical wind direction standard deviations crB and erg have a direct causal influence on or and err (Draxler, 1976), they are a much more dependable way of characterising the upwind turbulence than an integral length scale. Therefore, in Table 2 the upstream turbulence is characterised by measurements of the roughness length zO, Monin-Obukhov scale L and uH and (TV. The average Jensen number in these experiments was Q/H = 0.01. 3.2. Velocity
measurements
within
the arrays
In order to get an indication of the overall array blockage and number of rows required before
Table 1. Turbulence length scales calculated for different detrending periods with the sonic anemometer at a height of 1 H. (Wind direction from the west) Averaging block time 40 min 5 min 48 s 24 s
L, (m)
L,. (m)
L, (m)
47.4 19.6 9.6 5.5
102 24.5 7.7 4.4
1.3 1.1 1.4 0.9
186
et al.
R. W. MACDONALD
Table 2. Experimental parameters for concentration measurements Experiment
z, (mm)
Open terrain (neutral) Open terrain (unstable) S/H = 1.5 array (i,, = 0.16) S/H = 0.5array (& = 0.44) S/H = 3.0 array (A,, = 0.063) S/H = 1.5 array (averaging time experiment)
L (m)
0~ (deg)
ed (deg)
Uu (m/s)
PG class
23 9.0 11
2440 -12 -34
11.2 15.0 11.6
6.9 6.2 6.0
4.3 3.1 4.6
D B C
4.6
-68
10.3
5.2
4.3
C
4.5
-11
14.3
5.6
2.1
B
-42
12.3
6.1
3.7
C
18
f 2
1.5 r 5 1
0.5
i :
Ii I
-
Normal Wind -Behind Cube
A Normal Wind - Behind Gap
0
45 Deg. Wind - Behind Cube
:
45 Deg. Wind - Behind Gap
.
Upvind Sonic
0
-5
0
u
5
15
20
25
Frontof Array
Fig. 2. Variation of normalised velocity at cube height with depth into the array
a steady-state mean velocity developed, mean velocity measurements were made between rows of cubes in the array with spacing S/H = 1.5. Two sonic anemometers were used, each at a height of 1H. The upstream anemometer was used to provide a reference free-stream velocity (U,) for normalising the velocity measured within the array, while within the array the sonic anemometer was located either behind a cube or behind a gap in each row (see the + symbols in Row 5 of Fig. 1). Figure 2 is a plot of normalised velocity measured in the array for winds perpendicular to, and at 45” to the front row. For a normal wind, the wind speed behind the gaps was considerably higher than that behind the cubes, as would be expected due to the recirculating wake behind individual cubes. Minimum speeds were observed after the fourth row, where the normalised velocity was 0.71 behind the gaps and 0.44 behind the cubes. For the 45’ wind direction, there was little difference between the velocity behind a cube and that behind a gap, suggesting that there was more uniform sheltering due to the cubes and less channelling of the flow between the gaps at this angle. At 45” the wind speed in the array quickly reduces to
approximately 0.6 times its freestream value, whereas in the case of a normal wind a minimum speed was not reached until the fourth row. Wind data for the same array, but in a staggered configuration, also indicated that the wind speed behind the gaps between cubes was larger than that measured behind the cubes. The wind speed stabilised at approximately the 4th row to 0.40 (behind cubes) and 0.65 (gaps between cubes). These results suggest that a near asymptotic flow condition is reached after the 4th row. Previous wind tunnel measurements of drag coefficients in arrays of cubes have also shown that a fetch of approximately five rows is required before an asymptotic limit of CD is obtained for this array density (Hussain and Lee, 1980). This indicates that an 8 x 8 array is sufficiently large for the flow inside to be representative of that in a much larger array. 3.3. Concentration
measurements
for
open-terrain
plumes
In order to provide a baseline with which to compare the plume dispersion in the cube arrays,
Dispersion
through
regular
arrays
of cubic structures
787
0
4
2
6
a
10
12
Y/H Fig. 3. Lateral
concentration
profile for plume in open terrain at x/H = 6.0 is Pasquill B (centreline indicated as dashed line).
10
1
??
Unstable
a
Neutral
1
25
,
stability
class
8
16 ?&
I
a
8 0
5
IO
20
15
30
35
40
45
X/H Fig. 4. Variation
of lateral
diffusion
parameter
with distance
from source for plumes in open terrain
1.2
10 1
. Neutral
0.8 Curve Fits
“\s-:-
”
??
0.4
0.2
0 0
5
15
10
20
25
xni Fig. 5. Variation
of plume centreline
concentration
with distance
from source for plumes in open terrain.
R. W. MACDONALD
788
cross-wind concentration profiles were obtained for plumes in the open terrain at the site with no cubes present. Two such experiments were conducted, one under conditions of neutral stability (Pasquill class D) and the other under moderate instability (class B). Meterological parameters are given in Table 2 for these experiments. In these experiments both the source and instruments were located at height H/2. Figure 3 shows a typical lateral plume profile averaged over 3 min at a distance of 6.0 H downwind of the source, with a Gaussian curve fitted using the method of least squares. The value of the plume horizontal standard deviation cY was found at various distances from the source. These were plotted on a graph of scaled plume variances for plumes in open terrain using power-law expressions for Pasquill-Gifford sigmas recommended by Martin (1976) for 10 min averages in rural terrain. In Fig. 4 the P-G sigmas are non-dimensionalised with a scale factor of H = 11.25 m, in accordance with the assumed nominal scaling (1: 10) of
a.
b.
et a/
all these
experiments.
For
a Jensen number of roughness length would then be about 11 cm. The effectiveness of the scaling is shown by the fact that the unstable condition data lie close to the class B stability curve. However, the results in neutral (class D) stability fall between the class C and class B stability curves and not on the class D curve. This is likely due to the fact that for this wind direction, the surface roughness length (23 mm) was higher than that of the other experiments and thus the scaling parameter z,,/H was not preserved. Figure 5 shows the variation of the maximum (plume centreline) non-dimensional concentration K, with non-dimensional distance from the source x/H, along with algebraic curves that provide an adequate fit to the open-terrain results. These two curves for the open terrain plumes are used in later sections to compare the results from concentration measurements in the cube arrays, in order to illustrate the relative dispersion.
z,/H= 0.01, the full-scale upstream
Row 1 profile (xfH = 3.5).
Row 3 profile @fH = 8.5)
Fig. 6. Lateral concentration profiles in the array with spacing S/H = 1.5. (a) Row 1 profile (x/H= 3.5); (b) Row 3 profile (x/H= 8.5). (UVIC sampler numbers indicated in (a). Dashed line indicates source position.)
Dispersion
through
regular
arrays
3.4. Concentration profiles in the array configurations
2
789
those from the open-terrain experiments in Fig. 4. A plot of CT~ vs distance for the S/H = 0.5 array is also shown in Fig. 9. Although at the short distances the oYs appear to fall in the B or A stability class, they are between B and C at the larger distances and are comparable to the open-terrain plume results. However, for x/H < 10, the lateral dispersion is much greater than that in the previous array or in the open terrain, suggesting that this compact array causes an initially larger dispersion than the other cases. A plot of the variation of non-dimensional concentration K, with non-dimensional travel distance x/H (Fig. 10) shows that the mean concentration in the S/H = 1.5 array is comparable to that for a plume in open terrain. Since it is known that the mean velocity is reduced by the presence of the array (Fig. 2), the vertical dispersion of the plume must be enhanced relative to the open terrain plume, since assuming a Gaussian plume model, we have approximately
Typical lateral concentration profiles measured in the three different array densities are shown in Figs 6-8. Figure 6 shows lateral profiles of concentration in the S/H = 1.5 array and Fig. 7 shows results in the S/H = 0.5 array. In these plots, the location of the cubes is shown (looking into the wind) to indicate whether the concentration was measured behind a cube or behind a gap. In each case, the plume profile averaged over 3 min was well represented by a Gaussian distribution and did not appear to be distorted by the presence of the cubes, even in the first few rows where one might expect some sort of bifurcation of the plume as it is swept around the cubes on impact with the first row. In Fig. 9 the standard deviation gY of the plume profiles are compared with the standard results for plumes in open terrain to show the relative diffusion. The results for S/H = 1.5 fall very close to the line for Pasquill stability class C, except there is some scatter for .x/H < 10. For this geometry, the lateral dispersion coefficient is not strongly affected by the presence of the array and the gYs are comparable to
0
of cubic structures
4
6
a
Y/H
a. Row 1 profile (x/H = 3.25).
0
2
4
6
8
Y/H
b. Row 4 profile (x/H = 7.75). Fig. 7. Lateral
plume concentration
profiles in the array with S/H = 0.5. (a) Row 1 profile (x/H = 3.25); (b) Row 4 profile (x/H = 7.75).
R. W. MACDONALD
790
2
0
4
6
6
10
et al.
14
12
16
18
20
Y/H
Row 6 profile (x/H = 18.5). Plume impact with gap in front row.
a.
-~
0.14
0.12
0
0
0.1
0.04
i
002 0 0
4
2
6
6
10
12
14
16
18
20
Y/H
b.
Row 6 profile (x/H = 18.5). Plume impact with cubes in front row
Fig. 8. Lateral plume concentration profiles in Row 6 of the array with S/H = 3.0. (a) Row 6 profile (x/N = 18.5). Plume impact with gap in front row;(b) Row 6 profile (x/H= 18.5). Plume impact with cubes in front row.
10 --
0
S/H=lSArray
A S/H=O.SArray
a --
01;
:
0
5
;
; 10
:
: 15
;
: 20
:
; 25
:
I 30
::: 35
; 40
: 45
X/H Fig. 9. Variation
of lateral
diffusion
parameter
with distance and 0.5.
from the source
for arrays
with S/H = 1.5
Dispersion through regular arrays of cubic structures
791
1.2
1
\
Open Terrain Neutral 0
0.8
S/H = 1.5 Array 0
=
S/n 0.5Array
2 0.6 ‘. =
0.4 0.2 0 4
2
Fig. IO. Variation
of plume
8
6
centreline
12
concentration with distance S/H = 1.5 and 0.5.
For the dense array with S/H = 0.5, Fig. 10 shows that although the data fall slightly below the openterrain results at short distances, at larger distances they are quite similar. This would tend to follow from the fact that although the oY values are larger then the open-terrain plume experiments at the shorter distances, they are similar for x/H > 10. For the array with S/H = 3.0, the source was placed upwind of a gap in half the tests and upwind of a cube in the other half, since for this array the initial dispersion of the plume impinging on the front rows was more sensitive to lateral source location. The lateral plume profiles measured in Row 6 (Fig. S), show differences in plume width for a plume initially impacting a cube and for a plume initially entering a gap in the impact row. Because of this variation in initial
14
from
16
the source
18
for arrays
with
dispersion, a,s show dependence on lateral source position, and seem to fall on two different curves in Fig. 11. For x/H > 10, the upper a,s are similar to an open-terrain plume in stability class B, while the lower aYs actually fall below the results for an open-terrain plume in neutral stability. The fact that under certain conditions the horizontal dispersion coefficient for x/H > 10 is less than that of a plume in open terrain may be due to effective sheltering by the array, which can reduce plume meander. Figure 12 shows the nondimensional concentration vs downwind distance for this array. The plume concentration was larger than either of the open-terrain plume cases. It appears that the sheltering effect of the array increases concentration by reducing both aY and the mean wind speed in the array (see equation (3)).
10 0
Source In Fmnt of Gap
A Source in Front of Buildings
9 8 7
20
25
x/H Fig. 11. Variation
of lateral
plume
diffusion
parameter with distance S/H = 3.0.
from the source
for array
with
R. W. MACDONALD et al
792
1.6
c 0
1.2
2
Source in Front of Gap Open Terrain Unstable Open Terrain Neutral
1
0.6
0.4
0
Fig. 12. Variation of plume centreline concentration with distance from the source S/H = 3.0. The o,,/H results for the array with S/H = 1.5 were compared with the results obtained by Davidson et al. (1995) for an array density also in the wake interference flow regime. It was found that the a,,/H values for the same x/H distance from the source are on average about 35% higher in the Davidson experiments. This may be a result of the longer averaging time, 1.5 min as opposed to 3 min here, and is consistent with equation (5) with p = - 0.2. 3.5. Vertical concentration projiles in the array with S/H = 1.5 In the present study vertical concentration profiles were obtained only for the S/H = 1.5 array. The detectors were mounted in a vertical arrangement at various heights below z = 2H, at a distance 0.5H behind the rows of cubes, while the source was located on the ground at a distance 2H upwind of the array. Figure 13 shows vertical profiles behind Rows 3 and 5. The profiles behind cubes and behind gaps are essentially the same. However, there is a substantial difference between the Row 3 and Row 5 profile results below z = H. In Row 3, a large peak in the profile occurs at ground level, while in Row 5 the vertical concentration profile is more uniform within the array canopy. This difference is likely caused by the effects of the horseshoe vortices in the impact row(s) which tend to sweep the lower part of the plume to ground level, while deeper in the array the intense turbulent mixing causes a more uniform distribution below the cube tops. A transition to the more uniform vertical distribution appears to occur somewhere between Rows 3 and 5 for this array. A reflected Gaussian profile was fitted to the vertical profiles in Fig. 13 using the form g=exp[-0.5(7)2]
for array
with
+exp[-0.5(y)‘]
(4)
where z,, is not necessarily the actual source height but is an effective source height providing the best fit. For Row 3, the effective source height was found to be 0.04 H while in Row 5 it was 0.75H. However, the oz values were nearly the same, 0.84H and 0.82H, respectively. If we define an effective plume height as + = oz + zss, then in Row 3 or = 0.88H while in Row 5, or = 1.57H. As noted by Davidson et al. (1995), these results suggest that the enhancement of vertical diffusion by the array is caused mainly by an effective lifting of the centre of mass of the plume. This is due to the deceleration of the mean wind in the front rows of the array, which results in a vertical velocity component and divergence of the streamlines to satisfy continuity (Jerram et al., 1995). 3.6. EfSect of averaging time on peak-to-mean concentration ratios
In atmospheric dispersion experiments, it is found that if a time record of concentration is broken up into smaller time intervals and the resulting individual means calculated, there will be some variation of the shorter period means due to non-stationarity. One of these will be a “maximum average” concentration for the sequence of shorter period means taken from the longer record. As the smaller time increment is decreased, the maximum average tends to increase, and vice versa. Mean concentrations for various sampling times can be dealt with on a relative basis, by comparing the maximum average for a shorter sampling time with the average of a longer sampling time which covers the shorter increment. This is usually referred to as the peak-to-mean (P/M) ratio and is not to be confused with the instantaneous peak-to-mean ratio which refers to concentration fluctuations, and tends to be much higher.
Dispersion through regular arrays of cubic structures
193
2 1.6 1.6 1.4 1.2 3' 0.6 0.6 0.4 0.2 0
0
0.5
1
1.5
2
2.5
2
2.5
C(z)lC(z=HR)
a)
0
1
0.5
15
C(z)/C(z=HR)
W Fig. 13. Vertical concentration
profiles in the array with S/H = 1.5. (a) Row 3 vertical profile; (b) Row 5 vertical profile
Run6
-6estFit
0.1 /
-I
0.1
1
100
IO Sampling Time (min)
Fig. 14. Normalised
maximum
average
concentration
In most theoretical and empirical studies of the effect of averaging time on peak concentration, results are presented in the form of a power-law function of time (5)
vs sampling
time in the array
where C1 and Cz are sampling times T1 and terrain, the exponent in the range - 1< p < concentration increases time.
with S!H = 1.5.
mean concentrations for Tz, respectively. In open p is a negative number 0, i.e. maximum average with decreasing averaging
194
R. W. MACDONALD
An analysis of peak-to-mean concentration vs averaging time was performed on a series of experiments in the fourth row of the array with S/H = 1.5 under stability class C. The maximum plume centreline concentration was found for averaging times of 15 min, 10 min, 5 min, 1 min, 30 s and 10 s, using a window of the appropriate sampling time and scanning the 15min concentration data records. The concentrations, in the form of concentration ratios, were then plotted against time on a log-log graph (Fig. 14). The results fall roughly along a line with average slope - 0.23. One can therefore determine the ratio of the maximum average concentration for an arbitrary sampling period T2 between 10 s and 15 min to the average concentration for a given sampling period T1 using equation (5) with p = -0.23. This is a remarkable result, since it refers to concentrations measured within the array canopy. Previous results in the literature were only applicable to plumes in open terrain above the roughness elements. A value of p = - 0.2 is often quoted in the literature for plumes in open terrain under conditions of neutral stability (e.g. Singer et al., 1963). The fact that the exponent for the array is the same as that in open terrain suggests that this behaviour is due to the large-scale turbulence features of the atmospheric boundary layer, and is not affected by the smaller scale turbulence within the array.
4. APPLICATION
TO DISPERSION
MODELLING
Gifford (1960, 1970) noted that the lateral plume variance is made up of a relative diffusion component and a meandering component with a: = a,’ + a:.
(6)
In time-averaged Gaussian plume models for open terrain, the meandering component tends to dominate at short distances from the source. In an urban array, the flow perturbations induced by the buildings, which have a length scale of order H, can also contribute significantly to the meandering component at short distances. The combination of meandering, wake entrainment and wake release can greatly enhance the lateral dispersion at short distances (Davidson et al., 1995) and this could be seen in the present experiments for x/H < 10 (Fig. 9). At greater distances, the diffusion is mainly caused by the large-scale turbulence (scale % H) in the atmospheric boundary layer; thus the individual buildings should become less important. Since the large scales are dictated by upstream turbulence as opposed to turbulence generated by the buildings, o’yat larger distances should be relatively independent of the array, and this behaviour was generally observed in most of the arrays for x/H > 10. In such cases one would expect cry to be mainly dependent on (T* measured upwind or well above the canopy, in accordance with Draxler’s
er al
(1976) expression ay =
( !
o*xf$-
L
where TL is the Lagrangian time scale and f (x/UT,) is an empirical function which varies from 1 at x = 0 to 0.8 at x = 100 m (Hanna et al., 1977). Vertical diffusion is also very much enhanced by the array, especially close to the source, and is some function of mean building height and array density. The sparse results obtained in this field study suggest that the vertical distribution of the plume is a reflected Gaussian within the array, in agreement with Davidson et al. (1995). Yersel et al. (1983) recommend that one can estimate the Gaussian gz from the Briggs’ (1973) urban curves, or the Pasquill-Gifford curves with the stability class shifted by one class more unstable, as is traditionally done for the final (far field) phase of plume dispersion. Near the source, however, one has to model the effective lifting of the plume centre of mass due to the diverging streamlines in the impact region.
5. CONCLUSIONS
Several general effects of regular arrays of cubic obstacles on plume dispersion behaviour have been identified. These include: (a) Deceleration of the mean flow field in the array results in a reduced mean advection velocity relative to the open terrain. (b) Deflection of mean streamlines over the array causes an effective lifting of the centre of mass of the plume and an enhancement of vertical mixing. This appears to increase oz. (c) Downwash of plume material in the impact region, possibly due to the horseshoe vortex system around individual buildings, causes ground level concentrations to be much higher than rooftop level concentrations in the front rows of the array. (d) The lateral concentration profile within the array canopy is a Gaussian curve. The individual cube wakes do not influence the shape of the time-averaged concentration distribution over periods of several minutes. (e) Lateral dispersion is initially enhanced in the denser arrays for x/H < 10, but is generally similar to open-terrain results for larger distances and may even be slightly less in sparse arrays due to sheltering, which reduces plume meander. (f) Mean plume centreline concentration in the arrays is generally similar to open-terrain plumes because the combination of increased vertical spread and reduction in mean velocity counteract one another. (g) Peak-to-mean ratios for different sampling times in the range from 10 s to 1.5 min obey similar laws to open-terrain plumes, suggesting the behaviour is due to large-scale upwind turbulence features.
Dispersion
through
regular
A Gaussian plume model for the time-averaged concentration in the near field of an urban array is a plausible model and has the merits of relative simplicity, requiring few input parameters. There are still considerable gaps in our knowledge, however. In particular, the details of the dependence of o,,, oz and mean advection velocity on building lay-out and wind direction is needed. Acknowledgements-The authors would like to acknowledge the Ministry of Defence, Protection and Life Sciences Division, Porton Down, for sponsoring this work under agreement 2044-014~CBDE. Thanks are due to Dr David Hall of the Building Research Establishment for his helpful discussions.
REFERENCES
Baechlin W., Theurer W. and Plate E. J. (1992) Dispersion of gases released near the ground in built up areas: experimental results compared to simple numerical modelling. J. Wind Eny. Ind. Aero. 41-44, 2121-2732. Briggs G. A. (1973) Diffusion estimation for small emissions. ATDL Contribution File No. 79, Air Resources Atmospheric Turbulence and Diffusion Laboratory, NOAA, Oak Ridge, Tennessee. Davidson M. J., Mylne K. R., Jones C. D., Phillips J. C., Perkins R. J., Fung J. C. H. and Hunt J. C. R. (1995) Plume dispersion through large groups of obstacles-a field investigation. Atmospheric Enoironment 29, 3245-3256. Draxler R. R. (1976) Determination of atmospheric diffusion parameters. Atmospheric Environment 10, 99-105. Gifford F. A. (1960) Peak to average concentration ratios according to a fluctuating plume dispersion model. Int. J. Air Wat. Pollut. 3, 253-260. Gifford F. A. (1970) Peak-to-mean concentration ratios according to a “top-hat” fluctuating plume model. Conference on Air Pollution Meteorology, Am. Met. Sot. and Air Pollut. Contr. Ass., Raleigh, North Carolina. Hanna S. R., Briggs G. A., Deardorff J., Egan B. A., Gifford F.A. and Pasqill F. (1977) AMS workshop on
arrays
795
of cubic structures
stability
classification
schemes.
Bull. Am. Mel. Sec. 58,
1305-1309. Hanna S. R., Brig@ G. A. and Hosker R. P. (1982) Handbook on Atmospheric L@ision. Publication DOE/TIC 11223, U.S. Department of Energy, Washington, District of Columbia. Higson H. L., Griffiths R. F., Jones C. D. and Biltoft C. (1995) Effect of atmospheric stability on concentration fluctuations and wake retention times for dispersion in the vicinity of an isolated building. Environmetrics 6, 571-581. Hosker R. P. (1984) Flow and diffusion near obstacles. In Atmospheric Science and Power Production (edited by Randerson D.), pp. 241-326. Technical Information Centre, US Department of Energy, Washington, District of Columbia. Hussain M. and Lee B. E. (1980) A wind tunnel study of the mean pressure forces acting on large groups of low-rise buildings. J. Wind Eny. Ind. Aero. 6, 207-225. Jerram N., Perkins R. J., Fung J. C. H, Davidson M. J., Belcher S. E. and Hunt J. C. R. (1995) Atmospheric flow through groups of buildings and dispersion from localised sources. In Wind CIimate in Cities (edited by Cermak J. E.), pp. 109 -130. Kluwer, Dordrecht. Martin D. 0. (1976) Comment on the change of concentration standard deviations with distance. J. Air Pollut. Control Ass. 26, 145-146. Meroney R. N. (1982) Turbulent diffusion near buildings. In Engineering Meteorology (edited by Plate E.), pp. 481-525. Elsevier, Amsterdam. Morris, H. M. (1955) Flow in rough conduits. Trans. ASCE 120, 373.-398. Singer I. A., Imai K. and Del Campo R. G. (1963) Peak to mean pollutant concentration ratios for various terrain and vegetation cover. J. Air Pollut. Control Ass. 13, 40-42. Theurer W. (1995) Point sources in urban areas: modelling of neutral gas clouds with semi-empirical models. In Proc. NATO Advanced Studies Institute, Wind Climate in Cities (edited by Cermak J. E.), pp. 485-502. Kluwer, Dordrecht. Turner J. (1973) Local authority housing: a comparative study of the land use and built form of 110 schemes. Arch. J. 1, 265-280. Yersel M., Gable R. and Morrill J. (1983) Short range dispersion experiments in an urban area. Atmospheric Enoironment 17, 275-282.
Annospheru.
PII: S1352-2310(96)00263-4
Environment Vol. 31, No. 6, pp. 783-795, 1997 Copyright s$’ 1996 Elsevier Swnce Ltd Printed in Great Britam All rights reserved 1352-2310’97 $1700 + 0.00
FIELD EXPERIMENTS OF DISPERSION THROUGH REGULAR ARRAYS OF CUBIC STRUCTURES and R. F. GRIFFITHS
R. W. MACDONALD
Environmental Technology Centre, UMIST, P.O. Box 88, Manchester M60 lQD, U.K.
and S. C. CHEAH Ministry of Defence, PLSD, Porton Down, Salisbury SP4 OJQ, U.K. (First received 10 April 1996 and in final
form
25 August 1996)
Abstract-To investigate the effect of plan area density on the near-field dispersion of pollutant plumes in built-up areas, scaled field measurements have been made of the dispersion of a plume released upwind of regular arrays of cubes of varying plan area density. It was found that the lateral concentration profiles were Gaussian in all cases. Close to the source, the lateral dispersion parameter oYwas increased, relative to that of a plume in open terrain and was highest for the most dense array. Despite the increased plume dimensions in the array, the reduction in advection velocity resulted in ground-level concentrations that were in general not too different from those of a plume in open terrain. This behaviour can be modelled by a Gaussian-plume-type expression for time-averaged concentration. Copyright c 1996 Elsevier Science Ltd Ke)) word index: Atmospheric diffusion, urban pollution, building effects, Gaussian plume. atmospheric boundary layer.
1. INTRODUCTION
Most studies of urban dispersion in the past have been concerned either with long-range urban dispersion, where the plume dimensions are much larger than the individual buildings, or short-range diffusion around single or small groups of buildings. Excellent reviews on the latter subject exist (Hosker, 1984; Meroney, 1982) and various working models can be found for longer-range urban diffusion (Hanna et al., 1982). It is only relatively recently that the short-range dispersion problem in urban environments has been systematically studied. This is a surprising state of affairs, given that the greatest potential for damage to human health occurs in the near-field of toxic releases in an urban environment. In a recent study of urban dispersion from point sources, Davidson et al. (1995) identified several important characteristics of near-field plume behaviour for point sources in a relatively sparse array of buildings (ratio of gap between buildings to building height S/H = 2). The importance of the relative size of the plume to the obstacle array was indicated and within this type of array, it was found that the lateral plume concentration profile remained Gaussian, while a reflected Gaussian was a plausible fit for the vertical distribution. The plume CJ,,Swere similar to those of a control plume, but the vertical growth was enhanced
within the array. The mean concentrations were also comparable to a control plume, a result shown to be consistent with a reduction of mean velocity within the array. Theurer (1995) and Baechlin et al. (1992) found that for more irregular arrays of buildings with aspect ratios greater than one, the near-field profiles were usually not Gaussian shaped, but were dominated by local building effects which sometimes caused a lateral shift of the plume. However, in the far field beyond the “radius of homogenisation”, the time-averaged behaviour of the plume was no longer affected by single obstacles, but was influenced globally by an effective roughness length zo. In this region a Gaussian plume model (GPM) again provided a good representation of the behaviour. Undoubtedly, a key factor in determining the nearfield plume dispersion behaviour is the plan area density of the buildings. It is well established that there are three different aerodynamic flow regimes which occur in arrays, depending on the building density. In regular arrays of cubic elements, the plan area density A,, is related to the gap between cubes S and their height H by 1 Aa’= (1 + LY/H)~’ 783
784
R. W. MACDONALD
Based on flow over separated and Lee,
the plan area density, proximity effects and arrays of cubic roughness, elements can be into three regimes (Morris, 1955; Hussain 1980):
(i) The isolated roughness flow regime occurs when A,, < 8-10% (S/H > 2.2-2.6). In this regime, the elements are sufficiently far apart that their flow separation bubbles reattach before the next element is reached. (ii) The wake interference flow regime occurs for element spacing values 9% < 1,, < 17% (1.2 < S/H < 2.4). In this case, the separation region behind each element does not have sufficient room to develop fully. (iii) The skimming flow regime exists for values of i,, > 15S21% (S/H < 1.2-1.6). Stable vortices are created behind the elements and the flow appears to skim on the crests of the elements. According to Turner (1973) many housing estates fall into the density range I,, = ll-20% (S/H = 1.2-2.0). Industrial estates are usually less dense. Therefore, in modelling urban dispersion it is necessary to look at all three flow regimes. Whereas Davidson et al. (1995) investigated an array with plan area density I,, = 11.1% in the wake interference regime, the current study extends this database to include arrays in all three aerodynamic flow regimes.
et al. 2. EXPERIMENTAL
2.1.
DETAILS
Field site und building models
The experiments were conducted at the UMIST Environmental Technology test site in Lancashire, Northwest England, where there are regular winds from the sea which is 2 km to the west of the test site. The surrounding terrain consists of light scrub brush and grass, which was kept mown to a height of a few centimetres for a distance of about 50 m upwind of the cube arrays. The surface roughness length z, was determined from wind measurements at the site and showed some dependence on the mean wind direction. For the predominant wind direction which was from the west to northwest, z, varied from about 5 to 25 mm. The building models were nominal cubes made of galvanised steel and were selected to represent a 1: 10 scale mode1 of a building of nominal height 10 m. Depending on the lay-out, up to 100 were used in the experiments. The face of the cubes was 1.15 m high and 1.10 m wide, giving a representative scale H = 1.125 m (so that HZ equals the frontal area of the cube). The arrays were set up in regular grid-iron arrangements in three array spacings: S/H = 0.5, 1.5 and 3.0 (Fig. 1). 2.2. Measurement apparatus A gas tracer of pure-grade propylene (C,H,) was released at a controlled flow rate from an open-ended hose 12 mm in diameter. The gas flow rate was measured using a float-type variable area rotameter. The low release flow rates employed in the experiments ensured that the gas was quickly diluted and that the passive diffusion phase of the tracer started near the source.
?? ?? ?? ?? ?? ?? ACI
:
:
:
:
mmmmmm i’ ;.i.i.;.m
6’ :
d
9’ :D b S/H=05
i.i.i.C.;.m i.i.L’i.C.m
??
??
??
??
??
??
i.i.i.i.;.m m ?? b+m
?? m
?? ?? ?? ?? ?? ?? a
s/H=15
Fig. 1. Geometry of the cube arrays studied with layout of UVICs indicated for the array with S/H = 1.5. (a) 8 x 8 array with S/H = 1.5; (b) detail of 10 x 10 array with S/H = 0.5; (c) detail of 7 x 7 array with S/H = 3.0 ( + : typical locations of anemometer to measure velocity behind cubes and gaps within the array).
Dispersion through regular arrays of cubic structures The propylene concentrations were measured with UVIC” (Ultra Violet Ion Collector) detectors of the research variety, made by Industrial Development Bangor (IDB) Limited. The UVICs detector is a type of photoionisation detector (PID) which has sensitivity down to 0.01 ppm by volume with a response time of about 0.02 s. A detailed description of this instrument and the calibration procedure is provided in Higson et al. (1995). Signals from the gas detectors were transmitted to the data acquisition computer using an FM telemetry system operating in the range 433.5-434.7 MHz. An A/D data acquisition system mounted in the microcomputer was used to convert the signals to discrete voltage data at a sampling frequency of 50 Hz. Upwind mean and fluctuating velocity components were measured by Gill Research ultrasonic anemometers positioned 6-10 H upwind of the various arrays at a height of 1H above the ground. The sonic anemometer sampled the three orthogonal components of velocity at a frequency of 21 Hz, with a response time of 0.1 s. The anemometer also provided instantaneous temperature readings which allowed the calculation of heat flux. A variety of software was written to calculate the mean velocity U,,, the mean wind direction 0, the standard deviation of horizontal wind direction bg, the standard deviation of vertical wind direction cm, the Monin-Obukhov length scale L, and the surface roughness parameter za, all evaluated at height H. 2.3. Experimental
procedure
and selection
of averaging time
The basic experiment involved laying out UVIC@ detectors behind each row of the array to monitor the lateral distribution of concentration as well as the change of concentration with depth in the array. A maximum of 10 instruments at a time were used in each row. The UVIC” detectors and source were set at a height of H/2, with the source a distance 2H upwind of the array. The detectors were located at a distance H/2 behind the cubes in each row except in the most dense array, where they were H/4 behind the cubes. Figure 1 shows the position of the source and detectors set up in the 8 x 8 array with spacing S/H = 1.5, along with details of the other two array geometries studied. The x-axis is aligned with the mean wind direction and is measured from the source position. Gas was released and sampled continuously for 15 min in each experiment. From each record of wind direction, the three-minute period with the least variation of mean wind was selected as the standard sampling period for all mean concentrations and mean wind speed values quoted below. There are several reasons for choosing a three-minute averaging time: (i) Three minutes is the longest period that the mean wind stayed in an effectively constant direction in all the experiments. (ii) The purpose of the experiments was to look at the effect of the arrays on the diffusion. Since the scale of the turbulence generated within the array is of order H/U (typically about 0.2 s), such a time scale is well averaged over three minutes. (iii) If one averages over longer periods such as 15-20 min, the random passage of large-scale eddies due to phenomena other than the boundary-layer generation of turbulence leads to slow variations in wind direction. The resulting lateral meandering of the plume tends to overwhelm the time-averaged diffusion induced by the cubes; so that the contribution of the array to by would not be discernible. (iv) The effect of averaging time on concentration has been examined and concentrations for averaging times between 10 s and 15 min. tend to follow a simple power law, equation (5). The measured concentrations were non-dimensionalised as follows: K, = 10-6CU,HZ/Q
(2)
785
where C is mean concentration in ppm, Q is source strength in m3 s- ’Ui, is the upwind velocity at cube height in m s- ’ and H is in m. The measurement uncertainty in the calculated value of K, was estimated to be about 16%.
3. RESULTS AND DISCUSSION 3.1. Turbulence
characteristics
upwind
of the array
Davidson et al. (1995) reported that plume statistics from their field and wind tunnel studies could be made to collapse onto non-dimensional curves using length scales of the upstream turbulence. Measurements of the integral length scales of the upstream turbulence were also made at the present test site and the results were found to be very sensitive to the sampling time used. The measured integral length scales are shown in Table 1 for the longitudinal direction (I,,), lateral direction (I,,) and vertical direction (L,). These were calculated from the autocorrelation function as discussed in Davidson et al. (1995). The longitudinal and lateral length scales vary by a factor of lo-20 depending on the averaging block times shown. The vertical length scale is relatively insensitive to the detrending process because this length scale is limited by the presence of the ground and there are no slow time variations in the vertical direction as there are in the horizontal directions. Given that the integral length scales calculated from fixed-point wind data are so strongly sensitive to the detrending procedures used, dispersion data in this paper were non-dimensionalised with the obstacle Hz instead of using turbulence length dimension scales. It would be inappropriate to use the integral length scales in the non-dimensionalisation since they are so variable, being dependent upon averaging time. Since the horizontal and vertical wind direction standard deviations crB and erg have a direct causal influence on or and err (Draxler, 1976), they are a much more dependable way of characterising the upwind turbulence than an integral length scale. Therefore, in Table 2 the upstream turbulence is characterised by measurements of the roughness length zO, Monin-Obukhov scale L and uH and (TV. The average Jensen number in these experiments was Q/H = 0.01. 3.2. Velocity
measurements
within
the arrays
In order to get an indication of the overall array blockage and number of rows required before
Table 1. Turbulence length scales calculated for different detrending periods with the sonic anemometer at a height of 1 H. (Wind direction from the west) Averaging block time 40 min 5 min 48 s 24 s
L, (m)
L,. (m)
L, (m)
47.4 19.6 9.6 5.5
102 24.5 7.7 4.4
1.3 1.1 1.4 0.9
186
et al.
R. W. MACDONALD
Table 2. Experimental parameters for concentration measurements Experiment
z, (mm)
Open terrain (neutral) Open terrain (unstable) S/H = 1.5 array (i,, = 0.16) S/H = 0.5array (& = 0.44) S/H = 3.0 array (A,, = 0.063) S/H = 1.5 array (averaging time experiment)
L (m)
0~ (deg)
ed (deg)
Uu (m/s)
PG class
23 9.0 11
2440 -12 -34
11.2 15.0 11.6
6.9 6.2 6.0
4.3 3.1 4.6
D B C
4.6
-68
10.3
5.2
4.3
C
4.5
-11
14.3
5.6
2.1
B
-42
12.3
6.1
3.7
C
18
f 2
1.5 r 5 1
0.5
i :
Ii I
-
Normal Wind -Behind Cube
A Normal Wind - Behind Gap
0
45 Deg. Wind - Behind Cube
:
45 Deg. Wind - Behind Gap
.
Upvind Sonic
0
-5
0
u
5
15
20
25
Frontof Array
Fig. 2. Variation of normalised velocity at cube height with depth into the array
a steady-state mean velocity developed, mean velocity measurements were made between rows of cubes in the array with spacing S/H = 1.5. Two sonic anemometers were used, each at a height of 1H. The upstream anemometer was used to provide a reference free-stream velocity (U,) for normalising the velocity measured within the array, while within the array the sonic anemometer was located either behind a cube or behind a gap in each row (see the + symbols in Row 5 of Fig. 1). Figure 2 is a plot of normalised velocity measured in the array for winds perpendicular to, and at 45” to the front row. For a normal wind, the wind speed behind the gaps was considerably higher than that behind the cubes, as would be expected due to the recirculating wake behind individual cubes. Minimum speeds were observed after the fourth row, where the normalised velocity was 0.71 behind the gaps and 0.44 behind the cubes. For the 45’ wind direction, there was little difference between the velocity behind a cube and that behind a gap, suggesting that there was more uniform sheltering due to the cubes and less channelling of the flow between the gaps at this angle. At 45” the wind speed in the array quickly reduces to
approximately 0.6 times its freestream value, whereas in the case of a normal wind a minimum speed was not reached until the fourth row. Wind data for the same array, but in a staggered configuration, also indicated that the wind speed behind the gaps between cubes was larger than that measured behind the cubes. The wind speed stabilised at approximately the 4th row to 0.40 (behind cubes) and 0.65 (gaps between cubes). These results suggest that a near asymptotic flow condition is reached after the 4th row. Previous wind tunnel measurements of drag coefficients in arrays of cubes have also shown that a fetch of approximately five rows is required before an asymptotic limit of CD is obtained for this array density (Hussain and Lee, 1980). This indicates that an 8 x 8 array is sufficiently large for the flow inside to be representative of that in a much larger array. 3.3. Concentration
measurements
for
open-terrain
plumes
In order to provide a baseline with which to compare the plume dispersion in the cube arrays,
Dispersion
through
regular
arrays
of cubic structures
787
0
4
2
6
a
10
12
Y/H Fig. 3. Lateral
concentration
profile for plume in open terrain at x/H = 6.0 is Pasquill B (centreline indicated as dashed line).
10
1
??
Unstable
a
Neutral
1
25
,
stability
class
8
16 ?&
I
a
8 0
5
IO
20
15
30
35
40
45
X/H Fig. 4. Variation
of lateral
diffusion
parameter
with distance
from source for plumes in open terrain
1.2
10 1
. Neutral
0.8 Curve Fits
“\s-:-
”
??
0.4
0.2
0 0
5
15
10
20
25
xni Fig. 5. Variation
of plume centreline
concentration
with distance
from source for plumes in open terrain.
R. W. MACDONALD
788
cross-wind concentration profiles were obtained for plumes in the open terrain at the site with no cubes present. Two such experiments were conducted, one under conditions of neutral stability (Pasquill class D) and the other under moderate instability (class B). Meterological parameters are given in Table 2 for these experiments. In these experiments both the source and instruments were located at height H/2. Figure 3 shows a typical lateral plume profile averaged over 3 min at a distance of 6.0 H downwind of the source, with a Gaussian curve fitted using the method of least squares. The value of the plume horizontal standard deviation cY was found at various distances from the source. These were plotted on a graph of scaled plume variances for plumes in open terrain using power-law expressions for Pasquill-Gifford sigmas recommended by Martin (1976) for 10 min averages in rural terrain. In Fig. 4 the P-G sigmas are non-dimensionalised with a scale factor of H = 11.25 m, in accordance with the assumed nominal scaling (1: 10) of
a.
b.
et a/
all these
experiments.
For
a Jensen number of roughness length would then be about 11 cm. The effectiveness of the scaling is shown by the fact that the unstable condition data lie close to the class B stability curve. However, the results in neutral (class D) stability fall between the class C and class B stability curves and not on the class D curve. This is likely due to the fact that for this wind direction, the surface roughness length (23 mm) was higher than that of the other experiments and thus the scaling parameter z,,/H was not preserved. Figure 5 shows the variation of the maximum (plume centreline) non-dimensional concentration K, with non-dimensional distance from the source x/H, along with algebraic curves that provide an adequate fit to the open-terrain results. These two curves for the open terrain plumes are used in later sections to compare the results from concentration measurements in the cube arrays, in order to illustrate the relative dispersion.
z,/H= 0.01, the full-scale upstream
Row 1 profile (xfH = 3.5).
Row 3 profile @fH = 8.5)
Fig. 6. Lateral concentration profiles in the array with spacing S/H = 1.5. (a) Row 1 profile (x/H= 3.5); (b) Row 3 profile (x/H= 8.5). (UVIC sampler numbers indicated in (a). Dashed line indicates source position.)
Dispersion
through
regular
arrays
3.4. Concentration profiles in the array configurations
2
789
those from the open-terrain experiments in Fig. 4. A plot of CT~ vs distance for the S/H = 0.5 array is also shown in Fig. 9. Although at the short distances the oYs appear to fall in the B or A stability class, they are between B and C at the larger distances and are comparable to the open-terrain plume results. However, for x/H < 10, the lateral dispersion is much greater than that in the previous array or in the open terrain, suggesting that this compact array causes an initially larger dispersion than the other cases. A plot of the variation of non-dimensional concentration K, with non-dimensional travel distance x/H (Fig. 10) shows that the mean concentration in the S/H = 1.5 array is comparable to that for a plume in open terrain. Since it is known that the mean velocity is reduced by the presence of the array (Fig. 2), the vertical dispersion of the plume must be enhanced relative to the open terrain plume, since assuming a Gaussian plume model, we have approximately
Typical lateral concentration profiles measured in the three different array densities are shown in Figs 6-8. Figure 6 shows lateral profiles of concentration in the S/H = 1.5 array and Fig. 7 shows results in the S/H = 0.5 array. In these plots, the location of the cubes is shown (looking into the wind) to indicate whether the concentration was measured behind a cube or behind a gap. In each case, the plume profile averaged over 3 min was well represented by a Gaussian distribution and did not appear to be distorted by the presence of the cubes, even in the first few rows where one might expect some sort of bifurcation of the plume as it is swept around the cubes on impact with the first row. In Fig. 9 the standard deviation gY of the plume profiles are compared with the standard results for plumes in open terrain to show the relative diffusion. The results for S/H = 1.5 fall very close to the line for Pasquill stability class C, except there is some scatter for .x/H < 10. For this geometry, the lateral dispersion coefficient is not strongly affected by the presence of the array and the gYs are comparable to
0
of cubic structures
4
6
a
Y/H
a. Row 1 profile (x/H = 3.25).
0
2
4
6
8
Y/H
b. Row 4 profile (x/H = 7.75). Fig. 7. Lateral
plume concentration
profiles in the array with S/H = 0.5. (a) Row 1 profile (x/H = 3.25); (b) Row 4 profile (x/H = 7.75).
R. W. MACDONALD
790
2
0
4
6
6
10
et al.
14
12
16
18
20
Y/H
Row 6 profile (x/H = 18.5). Plume impact with gap in front row.
a.
-~
0.14
0.12
0
0
0.1
0.04
i
002 0 0
4
2
6
6
10
12
14
16
18
20
Y/H
b.
Row 6 profile (x/H = 18.5). Plume impact with cubes in front row
Fig. 8. Lateral plume concentration profiles in Row 6 of the array with S/H = 3.0. (a) Row 6 profile (x/N = 18.5). Plume impact with gap in front row;(b) Row 6 profile (x/H= 18.5). Plume impact with cubes in front row.
10 --
0
S/H=lSArray
A S/H=O.SArray
a --
01;
:
0
5
;
; 10
:
: 15
;
: 20
:
; 25
:
I 30
::: 35
; 40
: 45
X/H Fig. 9. Variation
of lateral
diffusion
parameter
with distance and 0.5.
from the source
for arrays
with S/H = 1.5
Dispersion through regular arrays of cubic structures
791
1.2
1
\
Open Terrain Neutral 0
0.8
S/H = 1.5 Array 0
=
S/n 0.5Array
2 0.6 ‘. =
0.4 0.2 0 4
2
Fig. IO. Variation
of plume
8
6
centreline
12
concentration with distance S/H = 1.5 and 0.5.
For the dense array with S/H = 0.5, Fig. 10 shows that although the data fall slightly below the openterrain results at short distances, at larger distances they are quite similar. This would tend to follow from the fact that although the oY values are larger then the open-terrain plume experiments at the shorter distances, they are similar for x/H > 10. For the array with S/H = 3.0, the source was placed upwind of a gap in half the tests and upwind of a cube in the other half, since for this array the initial dispersion of the plume impinging on the front rows was more sensitive to lateral source location. The lateral plume profiles measured in Row 6 (Fig. S), show differences in plume width for a plume initially impacting a cube and for a plume initially entering a gap in the impact row. Because of this variation in initial
14
from
16
the source
18
for arrays
with
dispersion, a,s show dependence on lateral source position, and seem to fall on two different curves in Fig. 11. For x/H > 10, the upper a,s are similar to an open-terrain plume in stability class B, while the lower aYs actually fall below the results for an open-terrain plume in neutral stability. The fact that under certain conditions the horizontal dispersion coefficient for x/H > 10 is less than that of a plume in open terrain may be due to effective sheltering by the array, which can reduce plume meander. Figure 12 shows the nondimensional concentration vs downwind distance for this array. The plume concentration was larger than either of the open-terrain plume cases. It appears that the sheltering effect of the array increases concentration by reducing both aY and the mean wind speed in the array (see equation (3)).
10 0
Source In Fmnt of Gap
A Source in Front of Buildings
9 8 7
20
25
x/H Fig. 11. Variation
of lateral
plume
diffusion
parameter with distance S/H = 3.0.
from the source
for array
with
R. W. MACDONALD et al
792
1.6
c 0
1.2
2
Source in Front of Gap Open Terrain Unstable Open Terrain Neutral
1
0.6
0.4
0
Fig. 12. Variation of plume centreline concentration with distance from the source S/H = 3.0. The o,,/H results for the array with S/H = 1.5 were compared with the results obtained by Davidson et al. (1995) for an array density also in the wake interference flow regime. It was found that the a,,/H values for the same x/H distance from the source are on average about 35% higher in the Davidson experiments. This may be a result of the longer averaging time, 1.5 min as opposed to 3 min here, and is consistent with equation (5) with p = - 0.2. 3.5. Vertical concentration projiles in the array with S/H = 1.5 In the present study vertical concentration profiles were obtained only for the S/H = 1.5 array. The detectors were mounted in a vertical arrangement at various heights below z = 2H, at a distance 0.5H behind the rows of cubes, while the source was located on the ground at a distance 2H upwind of the array. Figure 13 shows vertical profiles behind Rows 3 and 5. The profiles behind cubes and behind gaps are essentially the same. However, there is a substantial difference between the Row 3 and Row 5 profile results below z = H. In Row 3, a large peak in the profile occurs at ground level, while in Row 5 the vertical concentration profile is more uniform within the array canopy. This difference is likely caused by the effects of the horseshoe vortices in the impact row(s) which tend to sweep the lower part of the plume to ground level, while deeper in the array the intense turbulent mixing causes a more uniform distribution below the cube tops. A transition to the more uniform vertical distribution appears to occur somewhere between Rows 3 and 5 for this array. A reflected Gaussian profile was fitted to the vertical profiles in Fig. 13 using the form g=exp[-0.5(7)2]
for array
with
+exp[-0.5(y)‘]
(4)
where z,, is not necessarily the actual source height but is an effective source height providing the best fit. For Row 3, the effective source height was found to be 0.04 H while in Row 5 it was 0.75H. However, the oz values were nearly the same, 0.84H and 0.82H, respectively. If we define an effective plume height as + = oz + zss, then in Row 3 or = 0.88H while in Row 5, or = 1.57H. As noted by Davidson et al. (1995), these results suggest that the enhancement of vertical diffusion by the array is caused mainly by an effective lifting of the centre of mass of the plume. This is due to the deceleration of the mean wind in the front rows of the array, which results in a vertical velocity component and divergence of the streamlines to satisfy continuity (Jerram et al., 1995). 3.6. EfSect of averaging time on peak-to-mean concentration ratios
In atmospheric dispersion experiments, it is found that if a time record of concentration is broken up into smaller time intervals and the resulting individual means calculated, there will be some variation of the shorter period means due to non-stationarity. One of these will be a “maximum average” concentration for the sequence of shorter period means taken from the longer record. As the smaller time increment is decreased, the maximum average tends to increase, and vice versa. Mean concentrations for various sampling times can be dealt with on a relative basis, by comparing the maximum average for a shorter sampling time with the average of a longer sampling time which covers the shorter increment. This is usually referred to as the peak-to-mean (P/M) ratio and is not to be confused with the instantaneous peak-to-mean ratio which refers to concentration fluctuations, and tends to be much higher.
Dispersion through regular arrays of cubic structures
193
2 1.6 1.6 1.4 1.2 3' 0.6 0.6 0.4 0.2 0
0
0.5
1
1.5
2
2.5
2
2.5
C(z)lC(z=HR)
a)
0
1
0.5
15
C(z)/C(z=HR)
W Fig. 13. Vertical concentration
profiles in the array with S/H = 1.5. (a) Row 3 vertical profile; (b) Row 5 vertical profile
Run6
-6estFit
0.1 /
-I
0.1
1
100
IO Sampling Time (min)
Fig. 14. Normalised
maximum
average
concentration
In most theoretical and empirical studies of the effect of averaging time on peak concentration, results are presented in the form of a power-law function of time (5)
vs sampling
time in the array
where C1 and Cz are sampling times T1 and terrain, the exponent in the range - 1< p < concentration increases time.
with S!H = 1.5.
mean concentrations for Tz, respectively. In open p is a negative number 0, i.e. maximum average with decreasing averaging
194
R. W. MACDONALD
An analysis of peak-to-mean concentration vs averaging time was performed on a series of experiments in the fourth row of the array with S/H = 1.5 under stability class C. The maximum plume centreline concentration was found for averaging times of 15 min, 10 min, 5 min, 1 min, 30 s and 10 s, using a window of the appropriate sampling time and scanning the 15min concentration data records. The concentrations, in the form of concentration ratios, were then plotted against time on a log-log graph (Fig. 14). The results fall roughly along a line with average slope - 0.23. One can therefore determine the ratio of the maximum average concentration for an arbitrary sampling period T2 between 10 s and 15 min to the average concentration for a given sampling period T1 using equation (5) with p = -0.23. This is a remarkable result, since it refers to concentrations measured within the array canopy. Previous results in the literature were only applicable to plumes in open terrain above the roughness elements. A value of p = - 0.2 is often quoted in the literature for plumes in open terrain under conditions of neutral stability (e.g. Singer et al., 1963). The fact that the exponent for the array is the same as that in open terrain suggests that this behaviour is due to the large-scale turbulence features of the atmospheric boundary layer, and is not affected by the smaller scale turbulence within the array.
4. APPLICATION
TO DISPERSION
MODELLING
Gifford (1960, 1970) noted that the lateral plume variance is made up of a relative diffusion component and a meandering component with a: = a,’ + a:.
(6)
In time-averaged Gaussian plume models for open terrain, the meandering component tends to dominate at short distances from the source. In an urban array, the flow perturbations induced by the buildings, which have a length scale of order H, can also contribute significantly to the meandering component at short distances. The combination of meandering, wake entrainment and wake release can greatly enhance the lateral dispersion at short distances (Davidson et al., 1995) and this could be seen in the present experiments for x/H < 10 (Fig. 9). At greater distances, the diffusion is mainly caused by the large-scale turbulence (scale % H) in the atmospheric boundary layer; thus the individual buildings should become less important. Since the large scales are dictated by upstream turbulence as opposed to turbulence generated by the buildings, o’yat larger distances should be relatively independent of the array, and this behaviour was generally observed in most of the arrays for x/H > 10. In such cases one would expect cry to be mainly dependent on (T* measured upwind or well above the canopy, in accordance with Draxler’s
er al
(1976) expression ay =
( !
o*xf$-
L
where TL is the Lagrangian time scale and f (x/UT,) is an empirical function which varies from 1 at x = 0 to 0.8 at x = 100 m (Hanna et al., 1977). Vertical diffusion is also very much enhanced by the array, especially close to the source, and is some function of mean building height and array density. The sparse results obtained in this field study suggest that the vertical distribution of the plume is a reflected Gaussian within the array, in agreement with Davidson et al. (1995). Yersel et al. (1983) recommend that one can estimate the Gaussian gz from the Briggs’ (1973) urban curves, or the Pasquill-Gifford curves with the stability class shifted by one class more unstable, as is traditionally done for the final (far field) phase of plume dispersion. Near the source, however, one has to model the effective lifting of the plume centre of mass due to the diverging streamlines in the impact region.
5. CONCLUSIONS
Several general effects of regular arrays of cubic obstacles on plume dispersion behaviour have been identified. These include: (a) Deceleration of the mean flow field in the array results in a reduced mean advection velocity relative to the open terrain. (b) Deflection of mean streamlines over the array causes an effective lifting of the centre of mass of the plume and an enhancement of vertical mixing. This appears to increase oz. (c) Downwash of plume material in the impact region, possibly due to the horseshoe vortex system around individual buildings, causes ground level concentrations to be much higher than rooftop level concentrations in the front rows of the array. (d) The lateral concentration profile within the array canopy is a Gaussian curve. The individual cube wakes do not influence the shape of the time-averaged concentration distribution over periods of several minutes. (e) Lateral dispersion is initially enhanced in the denser arrays for x/H < 10, but is generally similar to open-terrain results for larger distances and may even be slightly less in sparse arrays due to sheltering, which reduces plume meander. (f) Mean plume centreline concentration in the arrays is generally similar to open-terrain plumes because the combination of increased vertical spread and reduction in mean velocity counteract one another. (g) Peak-to-mean ratios for different sampling times in the range from 10 s to 1.5 min obey similar laws to open-terrain plumes, suggesting the behaviour is due to large-scale upwind turbulence features.
Dispersion
through
regular
A Gaussian plume model for the time-averaged concentration in the near field of an urban array is a plausible model and has the merits of relative simplicity, requiring few input parameters. There are still considerable gaps in our knowledge, however. In particular, the details of the dependence of o,,, oz and mean advection velocity on building lay-out and wind direction is needed. Acknowledgements-The authors would like to acknowledge the Ministry of Defence, Protection and Life Sciences Division, Porton Down, for sponsoring this work under agreement 2044-014~CBDE. Thanks are due to Dr David Hall of the Building Research Establishment for his helpful discussions.
REFERENCES
Baechlin W., Theurer W. and Plate E. J. (1992) Dispersion of gases released near the ground in built up areas: experimental results compared to simple numerical modelling. J. Wind Eny. Ind. Aero. 41-44, 2121-2732. Briggs G. A. (1973) Diffusion estimation for small emissions. ATDL Contribution File No. 79, Air Resources Atmospheric Turbulence and Diffusion Laboratory, NOAA, Oak Ridge, Tennessee. Davidson M. J., Mylne K. R., Jones C. D., Phillips J. C., Perkins R. J., Fung J. C. H. and Hunt J. C. R. (1995) Plume dispersion through large groups of obstacles-a field investigation. Atmospheric Enoironment 29, 3245-3256. Draxler R. R. (1976) Determination of atmospheric diffusion parameters. Atmospheric Environment 10, 99-105. Gifford F. A. (1960) Peak to average concentration ratios according to a fluctuating plume dispersion model. Int. J. Air Wat. Pollut. 3, 253-260. Gifford F. A. (1970) Peak-to-mean concentration ratios according to a “top-hat” fluctuating plume model. Conference on Air Pollution Meteorology, Am. Met. Sot. and Air Pollut. Contr. Ass., Raleigh, North Carolina. Hanna S. R., Briggs G. A., Deardorff J., Egan B. A., Gifford F.A. and Pasqill F. (1977) AMS workshop on
arrays
795
of cubic structures
stability
classification
schemes.
Bull. Am. Mel. Sec. 58,
1305-1309. Hanna S. R., Brig@ G. A. and Hosker R. P. (1982) Handbook on Atmospheric L@ision. Publication DOE/TIC 11223, U.S. Department of Energy, Washington, District of Columbia. Higson H. L., Griffiths R. F., Jones C. D. and Biltoft C. (1995) Effect of atmospheric stability on concentration fluctuations and wake retention times for dispersion in the vicinity of an isolated building. Environmetrics 6, 571-581. Hosker R. P. (1984) Flow and diffusion near obstacles. In Atmospheric Science and Power Production (edited by Randerson D.), pp. 241-326. Technical Information Centre, US Department of Energy, Washington, District of Columbia. Hussain M. and Lee B. E. (1980) A wind tunnel study of the mean pressure forces acting on large groups of low-rise buildings. J. Wind Eny. Ind. Aero. 6, 207-225. Jerram N., Perkins R. J., Fung J. C. H, Davidson M. J., Belcher S. E. and Hunt J. C. R. (1995) Atmospheric flow through groups of buildings and dispersion from localised sources. In Wind CIimate in Cities (edited by Cermak J. E.), pp. 109 -130. Kluwer, Dordrecht. Martin D. 0. (1976) Comment on the change of concentration standard deviations with distance. J. Air Pollut. Control Ass. 26, 145-146. Meroney R. N. (1982) Turbulent diffusion near buildings. In Engineering Meteorology (edited by Plate E.), pp. 481-525. Elsevier, Amsterdam. Morris, H. M. (1955) Flow in rough conduits. Trans. ASCE 120, 373.-398. Singer I. A., Imai K. and Del Campo R. G. (1963) Peak to mean pollutant concentration ratios for various terrain and vegetation cover. J. Air Pollut. Control Ass. 13, 40-42. Theurer W. (1995) Point sources in urban areas: modelling of neutral gas clouds with semi-empirical models. In Proc. NATO Advanced Studies Institute, Wind Climate in Cities (edited by Cermak J. E.), pp. 485-502. Kluwer, Dordrecht. Turner J. (1973) Local authority housing: a comparative study of the land use and built form of 110 schemes. Arch. J. 1, 265-280. Yersel M., Gable R. and Morrill J. (1983) Short range dispersion experiments in an urban area. Atmospheric Enoironment 17, 275-282.