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Wind tunnel experiment of tracer gas diffusion within unstable boundary layer over coastal region
Atmospheric Environment 36 (2002) 4757–4766
Wind tunnel experiment of tracer gas diffusion within unstable boundary layer over coastal region$ K. Sada Central Research Institute of Electric Power Industry, 2-11-1 Iwato-kita, 201-8511 Komae-shi, Tokyo, Japan Received 29 November 1999; received in revised form 16 November 2000; accepted 10 July 2002
Abstract A wind tunnel experiment was carried out to simulate stack gas diffusion within an unstable atmospheric boundary layer over a coastal region. The wind tunnel floor, 4 m leeward of the entrance of the test section, was heated to 901C over a length of 6 m in the streamwise direction, and wind tunnel experiments were performed under the flat plate condition with a prototype-to-model length scale ratio of 1200. Three similarity criteria of flow fields in the wind tunnel and in atmosphere, viz., bulk Richardson number, surface Reynolds number and the ratio of the Peclet number to the Richardson number, were considered in the wind tunnel experiment. Tracer gas was released along the coastline at a height of 10 cm, which corresponded to 120 m in height in atmosphere. The obtained wind tunnel experimental results of ground level concentration were compared with 30-min average values of the field experiments, viz., the data from the Tokai 82 field experiment. The maximum ground level concentration and its location were accurately simulated when there was close similarity between the wind tunnel and atmospheric flow conditions. The maximum concentration increased and occurred closer to the source when the level of convection was relatively stronger in atmosphere. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Atmospheric diffusion; Unstable stratified flow; Similarity law; Ground level concentration; Field observation
1. Introduction Unstable atmospheric boundary layers sometimes develop over the land area from coastlines when the wind blows nearly perpendicular to the coastlines from the sea area due to the effects of solar radiation. Gas released from stacks near the coastline diffuses into the unstable boundary layer and is transported to the ground surface more rapidly than that under thermally neutral conditions. These tracer gas diffusion phenomena have been modeled in a wind tunnel with a heated floor. Using a wind tunnel, Ogawa et al. (1975) simulated tracer gas diffusion around coastal areas under neutral, unstable, stable and elevated inversion $
This paper was presented at the Euromech meeting ‘‘Wind Tunnel Modelling of dispersion in Environmental Flows’’ Prague, 13–15 September 1999.
conditions. The variations of flow characteristics with stratification conditions and diffusion patterns of tracer gas from ground sources under sea breeze conditions were shown. Meroney et al. (1975) conducted wind tunnel experiments for a shoreline site. The flow characteristics under unstable stratification conditions were compared with those of atmosphere using the bulk Richardson number and heating ratio. Their wind tunnel experiments indicated that the ground level concentration under unstable stratification conditions over a land area increased more than three times over those under neutral conditions. Ogawa et al. (1981) simulated the sea breeze and visualized flow in the wind tunnel and observed active mixing of smoke near the ground surface. After the wind tunnel experiments mentioned above, wind tunnel facilities were constructed and applied not only to sea breeze conditions, but also unstable
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Nomenclature A B C cfm g L Q T; T DT U; U UN u xi z0 a e n
critical surface Reynolds number critical value of ratio of surface Peclet number to Richardson number mean concentration skin friction coefficient acceleration of gravity representative length scale for wind tunnel and atmosphere source strength of stack gas mean temperature and representative value, respectively temperature difference mean velocity and representative value, respectively free stream velocity in wind tunnel friction velocity coordinates (x: streamwise, y: horizontal, z: normal to wind tunnel floor) roughness length molecular diffusivity prototype-to-model length scale ratio kinematic viscosity of air
Subscripts p value in atmosphere m value in wind tunnel w value at measurement point nearest the ground
stratification conditions. These unstable stratification phenomena over flat terrain, excluding the sea area, are called convective or mixing layers. The reproduction of thermal effects on flow and tracer gas diffusion within the convective layer have been attempted in the wind tunnel (e.g., Ohba and Nakamura, 1986; Rau et al., 1991; Ohya et al., 1996). In such wind tunnel experiments, good agreements between the wind tunnel results and observed data were obtained when turbulence quantities determined in the wind tunnel, for instance, turbulence intensity and ground level concentration, were normalized using the convective velocity scale (Poreh and Cermak, 1984; Sada, 1996). However, it is necessary to take into account of the effects of nonuniform surface temperature distribution when modeling flow and tracer gas diffusion in coastal areas. The performance of the wind tunnel for reproducing sea breeze conditions was reviewed by Avissar et al. (1990), and the operating range and similarity criteria of wind tunnel facilities with respect to sea breeze conditions were indicated. However, the usefulness of these similarity criteria in the wind tunnel has not been sufficiently confirmed through comparison with field observations. In this study, wind tunnel experiments for coastal areas were performed following the similarity criteria indicated by Avissar et al. (1990), and the results were compared with those of the Tokai 82 field experiment (see below) under various unstable stratification conditions.
2. Field experiment Wind tunnel experiment results were compared with those obtained in the field experiment conducted around Tokai village, located about 130 km northeast of the Tokyo metropolitan area, in 1982 (Kakuta and Hayashi, 1986; Chino et al., 1985). The topographical features within the field experiment area are shown in Fig. 1. Because the maximum terrain height from sea level was about 30 m within the field experiment area, the terrain conditions were considered to be very close to those of a flat plate. In this field experiment, tracer gas observations were made during the daytime between 4 and 8 August 1982. Because field observations were made under clear and cloudy conditions, tracer gas diffusion was observed under a range of unstable stratification conditions. The total number of field experiment data sets obtained was 11. Each data set included meteorological data and tracer gas concentration obtained at different measurement times during the 5 day field experiment period. Mean wind directions observed at the height of tracer gas release during the observation period varied within 59–1221 clockwise from north, except in one data set. Furthermore, a non-lift balloon, set at a height of 150 m from the ground surface, moved westward from the release point, following an easterly wind, except in the one case noted above. Based on the wind direction mentioned above, in 10 of the 11 data sets of field observations, wind was deduced to be easterly,
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Fig. 1. Topography around field observation area. The eastern part is sea and terrain height of western land part is shown as bright area for less than 20 m and dark area for more than 20 m. The position of tracer gas release is indicated by ‘‘+’’ flag.
which was almost perpendicular to the coastline and the same wind direction as in wind tunnel experiments. Furthermore, observed meteorological data in the field experiment were inadequate for estimating the similarity criteria, as will be discussed in Section 3.2, in one of the above 10 data sets. For these reasons, nine data sets out of a total of 11 were selected for comparison with those of wind tunnel experiments. Tracer gas, SF6, was released near the coastline at 120 m in height from sea level, and the duration of release was 90 min in all nine-field observation data sets. The ground level concentration was obtained for the last 30 min of the period of tracer gas release. Tracer gas was sampled along the arcs on the ground with radiuses of about 0.6, 1–5, 10 and 15 km from the point of release. All the sampling positions were located at intervals of about 101 on all arcs, and the number of sampling points was 112. The meteorological observations, including the wind direction, velocity and temperature, were carried out around the tracer gas point of release. Temperature measurements at up to several hundred meters in height from the ground were performed using the rawinsondes and tethered balloons at Point 2 (1.5 km), Point 3 (2.5 km), Point 4 (3.6 km) and Point 5 (9.5 km) on the land area. All the distances indicated here in brackets are distances from the tracer gas point of release. These measurement points for temperature were located along a line almost perpendicular to the coastline, viz., almost directly west of the tracer gas point of release. Measurements of wind direction and velocity up to
about 1000 m in height from the ground were carried out using the pilot balloons at Point 1 (0 km) and Point 5 (9.5 km), where all the distances in brackets are the same values as in the case of temperature measurement, viz., the distances from the position of tracer gas release. Therefore, Point 1 was the position of tracer gas release and Point 5 was the same position as for temperature measurement. Because several measurements of temperature and wind were carried out during the 90 min of tracer gas release, mean values of these measurements were calculated and compared with those of wind tunnel experiments.
3. Wind tunnel experiment under unstable condition 3.1. Wind tunnel facility and measurements Experiments were conducted in the wind tunnel facility at Komae Research Lab. of CRIEPI. This wind tunnel has a 3 m-wide, 1.5 m-high and 20 m-long test section. It is necessary to form a thick thermal boundary layer on the wind tunnel floor and to prevent secondary flow which is inherent in the wind tunnel, in order to simulate the thermal internal boundary layer development of a coastal region. A free stream velocity of UN ¼ 1:3 m/s was employed and roughness elements with L-shaped cross sections were set on the wind tunnel floor at the entrance of the wind tunnel test section to satisfy the above requirements. According to these experiment conditions, a thick boundary layer, viz.,
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about 21 cm thick, was formed at the coastline in the wind tunnel. A weak stable temperature gradient, 91C/m at an elevated position, viz., above about 50 cm from the wind tunnel floor, was set above the unstable boundary layer in order to obtain horizontal uniform flow in the wind tunnel. With the length scale ratio being 1:1200, this is equivalent to almost constant potential temperature conditions in atmosphere, which in fact is close to the upper level stratification observed in the field experiments, as mentioned in Section 4.1. This stable temperature gradient was achieved using rod heaters placed horizontally at the entrance of the wind tunnel test section. Furthermore, double-layered walls were used, viz., additional walls made of acrylic plastic with 5 mm thickness were inserted into side faces of the wind tunnel test section to obtain a horizontally uniform temperature distribution. The wind tunnel floor was heated electrically to 901C starting at 4 m downstream of the entrance to the test section, and the heating length was 6 m in the streamwise direction. The position of the wind tunnel floor at which heating was started corresponded to the coastline in the field, and this model coastline was perpendicular to the mean wind direction. The heated wind tunnel floor was divided into 36 individually controlled sections. Furthermore, a 2 cm-thick aluminum plate was used to achieve uniform surface temperature distribution. Since temperature varied within the flow on the heated wind tunnel floor and the mean and fluctuation velocities were to be measured, a laser Doppler velocimeter (LDV) was used in this study. A four-beam, two-dimensional backscattering LDV system was employed. Light was supplied by a two-watt argon-ion laser, and transmitted through optical fiber to the probe within the wind tunnel test section. The LDV probe was 14 mm in diameter with a 50 mm focal length. Particles (water and glycerin mixture) that scatter the laser beam were released from the upwind position of the wind tunnel test section. Two burst spectral analyzers were used to process LDV signals. More than 10,000 LDV signals were obtained at each point in a sampling period in excess of 30 s and with velocity bias compensation. Three directional components of mean and fluctuation velocities were measured in this study. Temperature was measured using a resistance thermometer with a single wire probe of 5 mm diameter, and average values were obtained. The position of tracer gas release was located 4 m downstream of the entrance of the wind tunnel test section, and at the horizontal center of the wind tunnel test section y ¼ 0 m. The model stack was located on the coastline, x ¼ 0 m, where heating of the wind tunnel floor began. A mixture of air and ethylene (C2H4) was released from the model stack as the tracer gas. Tracer gas was released from the height of 10 cm, viz., the
elevated source, corresponding to the height of tracer gas release in the field, viz., 120 m. Gas samples were collected at the ground surface and mean concentrations were measured using flame ionization detectors. 3.2. Similarity criteria with atmosphere Three similarity criteria between the wind tunnel and atmosphere were considered in this study following Avissar et al. (1990). The first criterion is based on the bulk Richardson number (¼ gL DT=TU2 ; see nomenclature for definitions of variables) which represents the ratio of the buoyancy effect caused by the temperature difference to the flow inertial force. When the same values of the bulk Richardson number are attained for the wind tunnel and atmosphere, DTp 1 Up 2 ¼ ð1Þ DTm e Um is obtained. Because the same values were assumed for the representative temperatures of the wind tunnel and atmosphere, viz., Tm ¼ Tp ; these values do not appear in Eq. (1) explicitly. Here, DTm is the temperature difference between the heated floor (land area) and unheated floor (sea area) in wind tunnel experiments. Because the temperature of the heated wind tunnel floor was 901C and that of the unheated floor was about 201C, DTm was 701C, which remained constant in the wind tunnel experiment. The temperature of the ground surface was not measured in the field observations. The nearest observed values, obtained using rawinsondes and tethered balloons, to the sea and ground surface, about 1 m from the surface, were used as representative values for the temperature difference for the atmosphere. These observed values of temperature used to determine the representative temperature difference for the atmosphere were averaged from several measurements carried out during tracer gas release. Therefore, the values of DTp were not constant and varied according to meteorological conditions and data sets of field observations. The velocity at the height of tracer gas release was used as the representative value. However, since the velocity difference between the height of tracer gas release and the free stream was small, the latter was used in the wind tunnel as the representative velocity, viz., Um ¼ UN : Wind velocity at the height of tracer gas release was used as the representative value, viz., Up ; in Eq. (1). These representative velocity values in the atmosphere were also averaged values of several measurements made during the 90 min of tracer gas release. Therefore, the values of Up were not constant and varied according to meteorological conditions and data sets of field observation. The second criterion is based on the surface Reynolds number (¼ u z0 =n), and ensures a fully rough flow when a large enough surface Reynolds number (u z0 =n > A) is
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achieved. To fulfill this criterion, DTp 1 cfm Up z0p 2 o DTm e3 2 nA
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ð2Þ
must be satisfied. The friction velocity used to determine the surface Reynolds number was expressed as the skin 2 friction coefficient applying the relation cfm ¼ 2u2m =UN ; and cfm was assumed to be 0.005 following Avissar et al. (1990). The friction velocity estimated from the vertical gradient of the mean wind velocity measured on the coastline in the wind tunnel was u =UN ¼ 0:043: When using this value, almost the same value of the friction coefficient as was used in Eq. (2) was obtained. The values for kinematic viscosity and critical surface Reynolds number were also taken from Avissar et al. (1990), viz., n ¼ 1:5 105 m2/s and A ¼ 1; respectively. Next, it is necessary to determine the values of the roughness length in atmosphere, z0p ; in Eq. (2). The field observation area is comprised of cultivated land, woodland, and residential and commercial areas with buildings several 10 m in height. In such situations, the roughness length in atmosphere is considered to vary from about one meter at the center of town to about 10 cm in areas covered with trees and grass. For this reason, it is difficult to determine the sole representative roughness length in atmosphere. Therefore, representative temperature differences of atmosphere were calculated using Eq. (2) with various roughness lengths in the range from 0.1 to 0.5 m. The third criterion is based on the ratio of the surface Peclet number (Pe ¼ u L=a) to the surface Richardson number (Ri ¼ gL DT=Tu2 ), i.e., relative rates of turbulent mixing to molecular diffusion. When a large value of this ratio (Pe =Ri > B) is achieved, DTp 1 cfm DTm 1=3 2 o Up ð3Þ Tp e 2ðgaBÞ2=3 Tm is obtained, which represents the enhancement of turbulent diffusion over molecular diffusion. This third criterion implies that the surface Peclet number is large enough and actually constraint (3) is not very important, as seen later, viz., Fig. 2. The critical value of the ratio of the surface Peclet number to Richardson number was taken from Avissar et al. (1990), viz., B ¼ 0:14: The representative temperatures used in Eq. (3) were the temperature of the wind tunnel floor at an unheated position, viz., Tm ¼ Tp ¼ 20 (1C). Next, the molecular diffusivity a between tracer gas, C2H4, and air was estimated to be 1.6 105 (m2/s) following the empirical evaluation method (The Society of Chemical Engineers Japan, 1978). Considering the three similarity criteria and the performance of the wind tunnel facility, wind tunnel experiments were conducted under the conditions of Um ¼ 1:3 m/s, DTm ¼ 701C and e ¼ 1200: Under these
Fig. 2. Representative temperature difference and velocity of atmosphere, obtained by applying three similarity criteria to unstable stratification condition in wind tunnel. The bold line corresponds to Eq. (1). The solid lines correspond to Eq. (2) with various roughness lengths, viz., z0p ¼ 0:5; 0.3, 0.2 and 0.1 m in downward direction. The bold dotted line corresponds to Eq. (3). The circles refer to field observations, open circles for cases corresponding to the wind tunnel simulation and shaded circles for remaining, more unstable cases.
conditions, Eqs. (1)–(3) were applied to estimate the relation between the representative temperature difference and representative wind velocity in atmosphere. The result is shown in Fig. 2. The values of the representative temperature difference and representative wind velocity for field observations are summarized in Table 1 and also plotted in Fig. 2. A more unstable stratification than that in the wind tunnel was observed for four of the nine field observation data sets. However, almost the same unstable stratification as that in the wind tunnel at z0p ¼ 0:3 m was observed for the remaining five field observation data sets. Although uncertainty remains in the determination of the roughness length in the atmosphere, it was concluded that almost the same unstable stratification was reproduced in the wind tunnel facility as those in the cases of the five field observation data sets. The wind tunnel results and
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Table 1 Representative velocity and temperature difference for field observations and wind tunnel Field observation
Wind tunnel
Run
Up (m/s)
DTp (1C)
(2) (3) 4 (5) 6 7 8 (9) 10
3.0 4.5 4.2 2.2 3.8 4.8 4.0 3.8 5.0
4.69 3.44 0.75 1.19 1.13 0.76 0.61 1.56 1.68
Um (m/s)
DTm (1C)
1.3
70
The run numbers within brackets indicate cases when more unstable stratifications are observed in field observations than in wind tunnel.
Fig. 3. Wind velocity and three directional turbulence intensity profiles for wind tunnel at coastline, x ¼ 0 km.
field observations are compared mainly for such cases, viz., almost the same stratification conditions, in Sections 4.2 and 4.3 below.
4. Wind tunnel experiment results 4.1. Measurement results at coastline in wind tunnel Mean wind and three directional turbulence intensity profiles at x ¼ 0 m, the coastline in the wind tunnel, are shown in Fig. 3. The vertical distance from the ground is measured assuming a length scale ratio of 1200. The boundary layer thickness was about 250 m and the tracer gas point of release, 120 m, was within the boundary layer. The power law, Upzp ; was applied to the vertical wind profile, and its coefficient, p; was about 1/9 at the
coastline. The power law coefficient obtained was smaller than that obtained under a flat plate condition with grass and woodland, viz. 1/7, and a smaller value was observed when roughness length was small, viz., the wind blew from the sea landward. All three directional turbulence intensities were increased in the vicinity of the ground within the turbulent boundary layer. The streamwise component of turbulence intensity was the highest and the vertical one was the lowest along the coastline. On the other hand, at an inland position, viz., x ¼ 7:08 km, the vertical component increased considerably, due to the active turbulent mixing caused by unstable stratification, and became higher than other components at the height midway through the boundary layer (e.g., Sada, 1996). Because a weak stable temperature gradient was set in the wind tunnel, it was apparent that an almost constant temperature was observed at the coastline of the wind tunnel, considering the Richardson number equivalence at an elevated position. However, vertical temperature distributions were not obtained at the coastline in the field observations; the profiles at the observed point nearest the coastline, viz., x ¼ 1:5 km from the tracer gas point of release, are shown in Fig. 4 for all nine field observation data sets used. The temperature observed in the field experiment was converted to a potential temperature using the dry adiabatic lapse rate and the difference from the value at the measurement point nearest the ground surface was indicated. Although weak stable stratification was observed at an elevated position, the potential temperature difference between the ground and z ¼ 300 m was less than 21C and almost the same neutral potential temperature profiles, viz., a constant value of z; were obtained for some field experiment data sets. For these reasons, the effect of stable stratification of inflow was considered to be small and could be negligible in some cases. In contrast, the observed bulk Richardson number obtained for a stable stratified flow at Great Lake (Meroney et al., 1975) was large and varied between 1.25 and 1.5. However, values of around 0.05 were obtained by applying the same definition of bulk Richardson number between the ground and z ¼ 200 m, with averaged values of DTp ¼ 0:121C and Up ¼ 4 m/s, as were obtained from Fig. 4 and shown in Table 1 for field experiments. According to these reasons, a strong stable stratified flow was not formed in the wind tunnel experiment, and only a very weak stable stratified temperature gradient, viz., 91C/m at an elevated position, was generated to prevent secondary flow. 4.2. Flow measurement and comparison with field observation Mean wind velocity profiles were normalized by the representative wind velocity and are shown in Fig. 5.
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Mean wind velocity profiles for field observations were derived from average values of several observations that were made during tracer gas release. Although the mean wind direction in the wind tunnel was always perpendi-
Fig. 4. Potential temperature profile for field observations at measurement point nearest the position of tracer gas release, viz., Point 2.
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cular to the coastline, that of atmosphere varied with time. Mean velocity values in the atmosphere indicated in Fig. 5 were not all components in the east–west direction, viz., perpendicular to the coastline, but the vector values included those in the horizontal direction. However, the direction of the mean wind in the field observations varied around the wind direction of 901, viz., perpendicular to the coastline, as indicated in Fig. 6. The deviation from 901 around the height of tracer gas release was less than about 301. For this reason, differences caused by deviations of the mean velocity might be small and wind velocity profiles obtained for atmosphere and the wind tunnel could be compared. Mean velocity profiles in Fig. 5 correspond to the five cases in which the three similarity criteria described in Section 3.2 were satisfied. The values of wind velocity in the wind tunnel showed good agreement to those of atmosphere, due to the fact that wind velocity was normalized with the corresponding reference velocity at the tracer gas point of release, viz., Point 1, and x ¼ 0 km for atmosphere and the wind tunnel, respectively. The profiles of wind velocity also agreed with each other at the tracer gas point of release. The same value of reference velocity was also used to normalize wind velocity at an inland area, viz., at Point 5 and x ¼ 7:08 km for atmosphere and the wind tunnel, respectively. However, wind velocity variations from the coastline to inland positions were not very large and almost the same profiles were obtained. For this reason, discrepancies in the wind velocity profiles between atmosphere and the wind tunnel were not so large, and almost the same profiles were obtained, as indicated in Fig. 5.
Fig. 5. Mean velocities of field observations and wind tunnel. The solid line with open circles and dotted line with shaded circles correspond to field observations at Point 1 and Point 5, respectively. The bold line and bold dotted line correspond to wind tunnel at x ¼ 0 and 7.08 km, respectively. Almost coincident profiles near the surface are obtained between field observations and wind tunnel experiments.
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Fig. 6. Wind direction observed around the height of tracer gas release. Open and shaded circles indicate wind directions in field observations at z ¼ 100 and 150 m, respectively. The line indicates wind direction in wind tunnel.
Because of the difficulty in determining the ground surface temperature of the whole field observation area, temperature was normalized using the values measured nearest the ground surface, viz., Tw ; equivalent observed heights were about 1 and 6 m from the ground surface for atmosphere and the wind tunnel, respectively. The results are shown in Fig. 7. With the normalization of temperature applied, temperature variations with height are enlarged and it is straightforward to compare the profiles between the wind tunnel and field observations. Temperature profiles obtained from field observations were also average values of several observations made during the tracer gas releases. Temperature profiles in Fig. 7 correspond to the five cases in which the three similarity criteria described in Section 3.2 were satisfied. An unstable temperature gradient was observed for both atmosphere and the wind tunnel near the ground surface. Temperature profiles of the wind tunnel showed good agreement with those of atmosphere near the coastline, viz., Point 3 and x ¼ 2:5 km for atmosphere and the wind tunnel, respectively. On increasing distance from the coastline, viz., at Point 5 in atmosphere, the temperature increased near the ground in some cases, viz., runs 4 and 6. This was due to active turbulent mixing near the ground surface, and vertically uniform temperature profiles tended to be enhanced. On increasing the distance from the coastline, viz., at x ¼ 7:08 km in the wind tunnel, the thickness of the thermal boundary layer was enlarged and the regions with an unstable temperature gradient reached almost several hundred meters from the ground. On the other hand, in
Fig. 7. Temperature in field observations and wind tunnel. The solid lines with open and shaded circles correspond to field observations at Point 3 and Point 5, respectively. The bold line and bold dotted line correspond to wind tunnel at x ¼ 2:5 and 7.08 km, respectively. Almost coincident values near the surface are obtained for wind tunnel experiments at x ¼ 2:5 and 7.08 km, and closer to field observations.
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atmosphere, because weak stable temperature gradients were observed at elevated positions, increase of the thickness of the thermal boundary layer was suppressed. Consequently, some discrepancies arose at elevated positions. However, such discrepancies were limited to elevated positions; almost the same temperature profiles were obtained at regions near the ground at an inland area. 4.3. Ground level concentration measurement and comparison with field experiment The ground level concentration of tracer gas, normalized by the source strength and representative wind velocity, is shown in Fig. 8 together with those of field observations. Ground level concentrations in Fig. 8 correspond to the five cases in which the three similarity criteria described in Section 3.2 were satisfied. Maximum values of ground level concentration at each sampling arc, viz., not the sampling points located west of the point of tracer gas release, were used as field observation data. However, maximum values were observed at sampling points located nearly perpendicular to the coastline. Ground level concentration obtained from wind tunnel experiments showed the maximum
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value at around x ¼ 2:5 km, and smoothly varied with distance from the tracer gas point of release. On the other hand, because ground level concentrations in field observations were obtained at discrete sampling points and were affected by the variation of meteorological conditions, viz., wind velocity and wind direction, scatter was observed in the data. However, ground level concentrations observed in the field were distributed around that obtained in the wind tunnel, and disagreement from the wind tunnel value was not large. The maximum ground level concentration and the observed distance in the field were normalized with those in the wind tunnel, considering a length scale ratio of 1200, and are indicated in Fig. 9. Normalized concentrations were larger than unity and normalized distances were less than unity when the three similarity criteria were not satisfied. In such cases, released tracer gas tended to reach the ground surface more rapidly, and concentrations tended to increase compared with those in the wind tunnel. However, normalized concentrations and distances were around unity when the three similarity criteria were satisfied. This was due to the fact that the ground level concentrations obtained in field observations were well simulated by the wind tunnel when similarity criteria were satisfied.
Fig. 8. Normalized ground level concentration with source strength and representative velocity for field observations and wind tunnel. The solid line and the circles correspond to wind tunnel and field observations, respectively.
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observations were well simulated in the wind tunnel when the three similarity criteria were satisfied.
References
Fig. 9. Maximum ground level concentration and its location in field observations normalized with those in wind tunnel. The open and shaded circles indicate cases when three similarity criteria are satisfied and not satisfied, respectively.
5. Conclusions In the present study, wind tunnel experiments under unstable conditions were conducted by heating the wind tunnel floor to simulate tracer gas diffusion over a coastal region. Three similarity criteria were used to define the unstable stratification condition in the wind tunnel. Consequently, five cases of field experiment data sets were inferred to indicate almost the same stratification condition as in the wind tunnel, and four remaining cases were inferred to be more unstable than that in the wind tunnel. Then, wind tunnel experiment results were compared with those of a field experiment conducted at Tokai village in 1982. The profiles of mean wind velocity and temperature obtained in the wind tunnel showed good agreement with those in atmosphere when the three similarity criteria were satisfied. Furthermore, it was revealed that maximum values of the ground level concentration and its observed distance from the position of tracer gas release obtained in field
Avissar, R., Moran, M.D., Wu, G., Meroney, R.N., Pielke, R.A., 1990. Operating ranges of mesoscale numerical models and meteorological wind tunnels for the simulation of sea and land breezes. Boundary-Layer Meteorology 50, 227–275. Chino, M., Ishikawa, H., Kakuta, M., 1985. Simulations of atmospheric dispersion in the existence of internal boundary layer by a three-layer model. Journal of the Japan Society Air Pollution 20 (3), 158–167 (in Japanese). Kakuta, M., Hayashi, T., 1986. Results of atmospheric diffusion experiments, Vol. 2, TOKAI 82 & TOKAI 83, Report No. JAERI-M 86-097, Japan Atomic Energy Research Institute (in Japanese). Meroney, R.N., Cermak, J.E., Yang, B.T., 1975. Modeling of atmospheric transport and fumigation at shoreline sites. Boundary-Layer Meteorology 9, 69–90. Ogawa, Y., Griffiths, R., Hoydysh, W.G., 1975. A wind-tunnel study of sea breeze effects. Boundary-Layer Meteorology 8, 141–161. Ogawa, Y., Diosey, P.G., Uehara, K., Ueda, H., 1981. A windtunnel for studying the effects of thermal stratification in the atmosphere. Atmospheric Environment 15 (5), 807–821. Ohba, R., Nakamura, S., 1986. Wind tunnel experiment of gas diffusion in thermally stratified flow. In: Proceedings of the Third EURASAP-International Workshop on Wind and Water Tunnel Modelling of Atmospheric Flow and Dispersion, Lausanne, pp. 57–63. Ohya, Y., Tatsuno, M., Nakamura, Y., Ueda, H., 1996. A thermally stratified wind tunnel for environmental flow studies. Atmospheric Environment. 30 (16), 2881–2887. Poreh, M., Cermak, J.E., 1984. Wind tunnel simulation of diffusion in a convective boundary layer. Boundary-Layer Meteorology 30, 431–455. Rau, M., Bachlin, W., Plate, E.J., 1991. Detailed design features of a new wind tunnel for studying the effects of thermal stratification. Atmospheric Environment 25A (7), 1257–1262. Sada, K., 1996. Wind tunnel experiment on flow and tracer gas diffusion in convective planetary boundary layer. JSME International Journal 39B (1), 19–27. The Society of Chemical Engineers Japan, 1978. Handbook of Chemical Engineering, 4th Edition. Maruzen, Tokyo, pp. 66–68 (in Japanese).
Wind tunnel experiment of tracer gas diffusion within unstable boundary layer over coastal region$ K. Sada Central Research Institute of Electric Power Industry, 2-11-1 Iwato-kita, 201-8511 Komae-shi, Tokyo, Japan Received 29 November 1999; received in revised form 16 November 2000; accepted 10 July 2002
Abstract A wind tunnel experiment was carried out to simulate stack gas diffusion within an unstable atmospheric boundary layer over a coastal region. The wind tunnel floor, 4 m leeward of the entrance of the test section, was heated to 901C over a length of 6 m in the streamwise direction, and wind tunnel experiments were performed under the flat plate condition with a prototype-to-model length scale ratio of 1200. Three similarity criteria of flow fields in the wind tunnel and in atmosphere, viz., bulk Richardson number, surface Reynolds number and the ratio of the Peclet number to the Richardson number, were considered in the wind tunnel experiment. Tracer gas was released along the coastline at a height of 10 cm, which corresponded to 120 m in height in atmosphere. The obtained wind tunnel experimental results of ground level concentration were compared with 30-min average values of the field experiments, viz., the data from the Tokai 82 field experiment. The maximum ground level concentration and its location were accurately simulated when there was close similarity between the wind tunnel and atmospheric flow conditions. The maximum concentration increased and occurred closer to the source when the level of convection was relatively stronger in atmosphere. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Atmospheric diffusion; Unstable stratified flow; Similarity law; Ground level concentration; Field observation
1. Introduction Unstable atmospheric boundary layers sometimes develop over the land area from coastlines when the wind blows nearly perpendicular to the coastlines from the sea area due to the effects of solar radiation. Gas released from stacks near the coastline diffuses into the unstable boundary layer and is transported to the ground surface more rapidly than that under thermally neutral conditions. These tracer gas diffusion phenomena have been modeled in a wind tunnel with a heated floor. Using a wind tunnel, Ogawa et al. (1975) simulated tracer gas diffusion around coastal areas under neutral, unstable, stable and elevated inversion $
This paper was presented at the Euromech meeting ‘‘Wind Tunnel Modelling of dispersion in Environmental Flows’’ Prague, 13–15 September 1999.
conditions. The variations of flow characteristics with stratification conditions and diffusion patterns of tracer gas from ground sources under sea breeze conditions were shown. Meroney et al. (1975) conducted wind tunnel experiments for a shoreline site. The flow characteristics under unstable stratification conditions were compared with those of atmosphere using the bulk Richardson number and heating ratio. Their wind tunnel experiments indicated that the ground level concentration under unstable stratification conditions over a land area increased more than three times over those under neutral conditions. Ogawa et al. (1981) simulated the sea breeze and visualized flow in the wind tunnel and observed active mixing of smoke near the ground surface. After the wind tunnel experiments mentioned above, wind tunnel facilities were constructed and applied not only to sea breeze conditions, but also unstable
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Nomenclature A B C cfm g L Q T; T DT U; U UN u xi z0 a e n
critical surface Reynolds number critical value of ratio of surface Peclet number to Richardson number mean concentration skin friction coefficient acceleration of gravity representative length scale for wind tunnel and atmosphere source strength of stack gas mean temperature and representative value, respectively temperature difference mean velocity and representative value, respectively free stream velocity in wind tunnel friction velocity coordinates (x: streamwise, y: horizontal, z: normal to wind tunnel floor) roughness length molecular diffusivity prototype-to-model length scale ratio kinematic viscosity of air
Subscripts p value in atmosphere m value in wind tunnel w value at measurement point nearest the ground
stratification conditions. These unstable stratification phenomena over flat terrain, excluding the sea area, are called convective or mixing layers. The reproduction of thermal effects on flow and tracer gas diffusion within the convective layer have been attempted in the wind tunnel (e.g., Ohba and Nakamura, 1986; Rau et al., 1991; Ohya et al., 1996). In such wind tunnel experiments, good agreements between the wind tunnel results and observed data were obtained when turbulence quantities determined in the wind tunnel, for instance, turbulence intensity and ground level concentration, were normalized using the convective velocity scale (Poreh and Cermak, 1984; Sada, 1996). However, it is necessary to take into account of the effects of nonuniform surface temperature distribution when modeling flow and tracer gas diffusion in coastal areas. The performance of the wind tunnel for reproducing sea breeze conditions was reviewed by Avissar et al. (1990), and the operating range and similarity criteria of wind tunnel facilities with respect to sea breeze conditions were indicated. However, the usefulness of these similarity criteria in the wind tunnel has not been sufficiently confirmed through comparison with field observations. In this study, wind tunnel experiments for coastal areas were performed following the similarity criteria indicated by Avissar et al. (1990), and the results were compared with those of the Tokai 82 field experiment (see below) under various unstable stratification conditions.
2. Field experiment Wind tunnel experiment results were compared with those obtained in the field experiment conducted around Tokai village, located about 130 km northeast of the Tokyo metropolitan area, in 1982 (Kakuta and Hayashi, 1986; Chino et al., 1985). The topographical features within the field experiment area are shown in Fig. 1. Because the maximum terrain height from sea level was about 30 m within the field experiment area, the terrain conditions were considered to be very close to those of a flat plate. In this field experiment, tracer gas observations were made during the daytime between 4 and 8 August 1982. Because field observations were made under clear and cloudy conditions, tracer gas diffusion was observed under a range of unstable stratification conditions. The total number of field experiment data sets obtained was 11. Each data set included meteorological data and tracer gas concentration obtained at different measurement times during the 5 day field experiment period. Mean wind directions observed at the height of tracer gas release during the observation period varied within 59–1221 clockwise from north, except in one data set. Furthermore, a non-lift balloon, set at a height of 150 m from the ground surface, moved westward from the release point, following an easterly wind, except in the one case noted above. Based on the wind direction mentioned above, in 10 of the 11 data sets of field observations, wind was deduced to be easterly,
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Fig. 1. Topography around field observation area. The eastern part is sea and terrain height of western land part is shown as bright area for less than 20 m and dark area for more than 20 m. The position of tracer gas release is indicated by ‘‘+’’ flag.
which was almost perpendicular to the coastline and the same wind direction as in wind tunnel experiments. Furthermore, observed meteorological data in the field experiment were inadequate for estimating the similarity criteria, as will be discussed in Section 3.2, in one of the above 10 data sets. For these reasons, nine data sets out of a total of 11 were selected for comparison with those of wind tunnel experiments. Tracer gas, SF6, was released near the coastline at 120 m in height from sea level, and the duration of release was 90 min in all nine-field observation data sets. The ground level concentration was obtained for the last 30 min of the period of tracer gas release. Tracer gas was sampled along the arcs on the ground with radiuses of about 0.6, 1–5, 10 and 15 km from the point of release. All the sampling positions were located at intervals of about 101 on all arcs, and the number of sampling points was 112. The meteorological observations, including the wind direction, velocity and temperature, were carried out around the tracer gas point of release. Temperature measurements at up to several hundred meters in height from the ground were performed using the rawinsondes and tethered balloons at Point 2 (1.5 km), Point 3 (2.5 km), Point 4 (3.6 km) and Point 5 (9.5 km) on the land area. All the distances indicated here in brackets are distances from the tracer gas point of release. These measurement points for temperature were located along a line almost perpendicular to the coastline, viz., almost directly west of the tracer gas point of release. Measurements of wind direction and velocity up to
about 1000 m in height from the ground were carried out using the pilot balloons at Point 1 (0 km) and Point 5 (9.5 km), where all the distances in brackets are the same values as in the case of temperature measurement, viz., the distances from the position of tracer gas release. Therefore, Point 1 was the position of tracer gas release and Point 5 was the same position as for temperature measurement. Because several measurements of temperature and wind were carried out during the 90 min of tracer gas release, mean values of these measurements were calculated and compared with those of wind tunnel experiments.
3. Wind tunnel experiment under unstable condition 3.1. Wind tunnel facility and measurements Experiments were conducted in the wind tunnel facility at Komae Research Lab. of CRIEPI. This wind tunnel has a 3 m-wide, 1.5 m-high and 20 m-long test section. It is necessary to form a thick thermal boundary layer on the wind tunnel floor and to prevent secondary flow which is inherent in the wind tunnel, in order to simulate the thermal internal boundary layer development of a coastal region. A free stream velocity of UN ¼ 1:3 m/s was employed and roughness elements with L-shaped cross sections were set on the wind tunnel floor at the entrance of the wind tunnel test section to satisfy the above requirements. According to these experiment conditions, a thick boundary layer, viz.,
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about 21 cm thick, was formed at the coastline in the wind tunnel. A weak stable temperature gradient, 91C/m at an elevated position, viz., above about 50 cm from the wind tunnel floor, was set above the unstable boundary layer in order to obtain horizontal uniform flow in the wind tunnel. With the length scale ratio being 1:1200, this is equivalent to almost constant potential temperature conditions in atmosphere, which in fact is close to the upper level stratification observed in the field experiments, as mentioned in Section 4.1. This stable temperature gradient was achieved using rod heaters placed horizontally at the entrance of the wind tunnel test section. Furthermore, double-layered walls were used, viz., additional walls made of acrylic plastic with 5 mm thickness were inserted into side faces of the wind tunnel test section to obtain a horizontally uniform temperature distribution. The wind tunnel floor was heated electrically to 901C starting at 4 m downstream of the entrance to the test section, and the heating length was 6 m in the streamwise direction. The position of the wind tunnel floor at which heating was started corresponded to the coastline in the field, and this model coastline was perpendicular to the mean wind direction. The heated wind tunnel floor was divided into 36 individually controlled sections. Furthermore, a 2 cm-thick aluminum plate was used to achieve uniform surface temperature distribution. Since temperature varied within the flow on the heated wind tunnel floor and the mean and fluctuation velocities were to be measured, a laser Doppler velocimeter (LDV) was used in this study. A four-beam, two-dimensional backscattering LDV system was employed. Light was supplied by a two-watt argon-ion laser, and transmitted through optical fiber to the probe within the wind tunnel test section. The LDV probe was 14 mm in diameter with a 50 mm focal length. Particles (water and glycerin mixture) that scatter the laser beam were released from the upwind position of the wind tunnel test section. Two burst spectral analyzers were used to process LDV signals. More than 10,000 LDV signals were obtained at each point in a sampling period in excess of 30 s and with velocity bias compensation. Three directional components of mean and fluctuation velocities were measured in this study. Temperature was measured using a resistance thermometer with a single wire probe of 5 mm diameter, and average values were obtained. The position of tracer gas release was located 4 m downstream of the entrance of the wind tunnel test section, and at the horizontal center of the wind tunnel test section y ¼ 0 m. The model stack was located on the coastline, x ¼ 0 m, where heating of the wind tunnel floor began. A mixture of air and ethylene (C2H4) was released from the model stack as the tracer gas. Tracer gas was released from the height of 10 cm, viz., the
elevated source, corresponding to the height of tracer gas release in the field, viz., 120 m. Gas samples were collected at the ground surface and mean concentrations were measured using flame ionization detectors. 3.2. Similarity criteria with atmosphere Three similarity criteria between the wind tunnel and atmosphere were considered in this study following Avissar et al. (1990). The first criterion is based on the bulk Richardson number (¼ gL DT=TU2 ; see nomenclature for definitions of variables) which represents the ratio of the buoyancy effect caused by the temperature difference to the flow inertial force. When the same values of the bulk Richardson number are attained for the wind tunnel and atmosphere, DTp 1 Up 2 ¼ ð1Þ DTm e Um is obtained. Because the same values were assumed for the representative temperatures of the wind tunnel and atmosphere, viz., Tm ¼ Tp ; these values do not appear in Eq. (1) explicitly. Here, DTm is the temperature difference between the heated floor (land area) and unheated floor (sea area) in wind tunnel experiments. Because the temperature of the heated wind tunnel floor was 901C and that of the unheated floor was about 201C, DTm was 701C, which remained constant in the wind tunnel experiment. The temperature of the ground surface was not measured in the field observations. The nearest observed values, obtained using rawinsondes and tethered balloons, to the sea and ground surface, about 1 m from the surface, were used as representative values for the temperature difference for the atmosphere. These observed values of temperature used to determine the representative temperature difference for the atmosphere were averaged from several measurements carried out during tracer gas release. Therefore, the values of DTp were not constant and varied according to meteorological conditions and data sets of field observations. The velocity at the height of tracer gas release was used as the representative value. However, since the velocity difference between the height of tracer gas release and the free stream was small, the latter was used in the wind tunnel as the representative velocity, viz., Um ¼ UN : Wind velocity at the height of tracer gas release was used as the representative value, viz., Up ; in Eq. (1). These representative velocity values in the atmosphere were also averaged values of several measurements made during the 90 min of tracer gas release. Therefore, the values of Up were not constant and varied according to meteorological conditions and data sets of field observation. The second criterion is based on the surface Reynolds number (¼ u z0 =n), and ensures a fully rough flow when a large enough surface Reynolds number (u z0 =n > A) is
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achieved. To fulfill this criterion, DTp 1 cfm Up z0p 2 o DTm e3 2 nA
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ð2Þ
must be satisfied. The friction velocity used to determine the surface Reynolds number was expressed as the skin 2 friction coefficient applying the relation cfm ¼ 2u2m =UN ; and cfm was assumed to be 0.005 following Avissar et al. (1990). The friction velocity estimated from the vertical gradient of the mean wind velocity measured on the coastline in the wind tunnel was u =UN ¼ 0:043: When using this value, almost the same value of the friction coefficient as was used in Eq. (2) was obtained. The values for kinematic viscosity and critical surface Reynolds number were also taken from Avissar et al. (1990), viz., n ¼ 1:5 105 m2/s and A ¼ 1; respectively. Next, it is necessary to determine the values of the roughness length in atmosphere, z0p ; in Eq. (2). The field observation area is comprised of cultivated land, woodland, and residential and commercial areas with buildings several 10 m in height. In such situations, the roughness length in atmosphere is considered to vary from about one meter at the center of town to about 10 cm in areas covered with trees and grass. For this reason, it is difficult to determine the sole representative roughness length in atmosphere. Therefore, representative temperature differences of atmosphere were calculated using Eq. (2) with various roughness lengths in the range from 0.1 to 0.5 m. The third criterion is based on the ratio of the surface Peclet number (Pe ¼ u L=a) to the surface Richardson number (Ri ¼ gL DT=Tu2 ), i.e., relative rates of turbulent mixing to molecular diffusion. When a large value of this ratio (Pe =Ri > B) is achieved, DTp 1 cfm DTm 1=3 2 o Up ð3Þ Tp e 2ðgaBÞ2=3 Tm is obtained, which represents the enhancement of turbulent diffusion over molecular diffusion. This third criterion implies that the surface Peclet number is large enough and actually constraint (3) is not very important, as seen later, viz., Fig. 2. The critical value of the ratio of the surface Peclet number to Richardson number was taken from Avissar et al. (1990), viz., B ¼ 0:14: The representative temperatures used in Eq. (3) were the temperature of the wind tunnel floor at an unheated position, viz., Tm ¼ Tp ¼ 20 (1C). Next, the molecular diffusivity a between tracer gas, C2H4, and air was estimated to be 1.6 105 (m2/s) following the empirical evaluation method (The Society of Chemical Engineers Japan, 1978). Considering the three similarity criteria and the performance of the wind tunnel facility, wind tunnel experiments were conducted under the conditions of Um ¼ 1:3 m/s, DTm ¼ 701C and e ¼ 1200: Under these
Fig. 2. Representative temperature difference and velocity of atmosphere, obtained by applying three similarity criteria to unstable stratification condition in wind tunnel. The bold line corresponds to Eq. (1). The solid lines correspond to Eq. (2) with various roughness lengths, viz., z0p ¼ 0:5; 0.3, 0.2 and 0.1 m in downward direction. The bold dotted line corresponds to Eq. (3). The circles refer to field observations, open circles for cases corresponding to the wind tunnel simulation and shaded circles for remaining, more unstable cases.
conditions, Eqs. (1)–(3) were applied to estimate the relation between the representative temperature difference and representative wind velocity in atmosphere. The result is shown in Fig. 2. The values of the representative temperature difference and representative wind velocity for field observations are summarized in Table 1 and also plotted in Fig. 2. A more unstable stratification than that in the wind tunnel was observed for four of the nine field observation data sets. However, almost the same unstable stratification as that in the wind tunnel at z0p ¼ 0:3 m was observed for the remaining five field observation data sets. Although uncertainty remains in the determination of the roughness length in the atmosphere, it was concluded that almost the same unstable stratification was reproduced in the wind tunnel facility as those in the cases of the five field observation data sets. The wind tunnel results and
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Table 1 Representative velocity and temperature difference for field observations and wind tunnel Field observation
Wind tunnel
Run
Up (m/s)
DTp (1C)
(2) (3) 4 (5) 6 7 8 (9) 10
3.0 4.5 4.2 2.2 3.8 4.8 4.0 3.8 5.0
4.69 3.44 0.75 1.19 1.13 0.76 0.61 1.56 1.68
Um (m/s)
DTm (1C)
1.3
70
The run numbers within brackets indicate cases when more unstable stratifications are observed in field observations than in wind tunnel.
Fig. 3. Wind velocity and three directional turbulence intensity profiles for wind tunnel at coastline, x ¼ 0 km.
field observations are compared mainly for such cases, viz., almost the same stratification conditions, in Sections 4.2 and 4.3 below.
4. Wind tunnel experiment results 4.1. Measurement results at coastline in wind tunnel Mean wind and three directional turbulence intensity profiles at x ¼ 0 m, the coastline in the wind tunnel, are shown in Fig. 3. The vertical distance from the ground is measured assuming a length scale ratio of 1200. The boundary layer thickness was about 250 m and the tracer gas point of release, 120 m, was within the boundary layer. The power law, Upzp ; was applied to the vertical wind profile, and its coefficient, p; was about 1/9 at the
coastline. The power law coefficient obtained was smaller than that obtained under a flat plate condition with grass and woodland, viz. 1/7, and a smaller value was observed when roughness length was small, viz., the wind blew from the sea landward. All three directional turbulence intensities were increased in the vicinity of the ground within the turbulent boundary layer. The streamwise component of turbulence intensity was the highest and the vertical one was the lowest along the coastline. On the other hand, at an inland position, viz., x ¼ 7:08 km, the vertical component increased considerably, due to the active turbulent mixing caused by unstable stratification, and became higher than other components at the height midway through the boundary layer (e.g., Sada, 1996). Because a weak stable temperature gradient was set in the wind tunnel, it was apparent that an almost constant temperature was observed at the coastline of the wind tunnel, considering the Richardson number equivalence at an elevated position. However, vertical temperature distributions were not obtained at the coastline in the field observations; the profiles at the observed point nearest the coastline, viz., x ¼ 1:5 km from the tracer gas point of release, are shown in Fig. 4 for all nine field observation data sets used. The temperature observed in the field experiment was converted to a potential temperature using the dry adiabatic lapse rate and the difference from the value at the measurement point nearest the ground surface was indicated. Although weak stable stratification was observed at an elevated position, the potential temperature difference between the ground and z ¼ 300 m was less than 21C and almost the same neutral potential temperature profiles, viz., a constant value of z; were obtained for some field experiment data sets. For these reasons, the effect of stable stratification of inflow was considered to be small and could be negligible in some cases. In contrast, the observed bulk Richardson number obtained for a stable stratified flow at Great Lake (Meroney et al., 1975) was large and varied between 1.25 and 1.5. However, values of around 0.05 were obtained by applying the same definition of bulk Richardson number between the ground and z ¼ 200 m, with averaged values of DTp ¼ 0:121C and Up ¼ 4 m/s, as were obtained from Fig. 4 and shown in Table 1 for field experiments. According to these reasons, a strong stable stratified flow was not formed in the wind tunnel experiment, and only a very weak stable stratified temperature gradient, viz., 91C/m at an elevated position, was generated to prevent secondary flow. 4.2. Flow measurement and comparison with field observation Mean wind velocity profiles were normalized by the representative wind velocity and are shown in Fig. 5.
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Mean wind velocity profiles for field observations were derived from average values of several observations that were made during tracer gas release. Although the mean wind direction in the wind tunnel was always perpendi-
Fig. 4. Potential temperature profile for field observations at measurement point nearest the position of tracer gas release, viz., Point 2.
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cular to the coastline, that of atmosphere varied with time. Mean velocity values in the atmosphere indicated in Fig. 5 were not all components in the east–west direction, viz., perpendicular to the coastline, but the vector values included those in the horizontal direction. However, the direction of the mean wind in the field observations varied around the wind direction of 901, viz., perpendicular to the coastline, as indicated in Fig. 6. The deviation from 901 around the height of tracer gas release was less than about 301. For this reason, differences caused by deviations of the mean velocity might be small and wind velocity profiles obtained for atmosphere and the wind tunnel could be compared. Mean velocity profiles in Fig. 5 correspond to the five cases in which the three similarity criteria described in Section 3.2 were satisfied. The values of wind velocity in the wind tunnel showed good agreement to those of atmosphere, due to the fact that wind velocity was normalized with the corresponding reference velocity at the tracer gas point of release, viz., Point 1, and x ¼ 0 km for atmosphere and the wind tunnel, respectively. The profiles of wind velocity also agreed with each other at the tracer gas point of release. The same value of reference velocity was also used to normalize wind velocity at an inland area, viz., at Point 5 and x ¼ 7:08 km for atmosphere and the wind tunnel, respectively. However, wind velocity variations from the coastline to inland positions were not very large and almost the same profiles were obtained. For this reason, discrepancies in the wind velocity profiles between atmosphere and the wind tunnel were not so large, and almost the same profiles were obtained, as indicated in Fig. 5.
Fig. 5. Mean velocities of field observations and wind tunnel. The solid line with open circles and dotted line with shaded circles correspond to field observations at Point 1 and Point 5, respectively. The bold line and bold dotted line correspond to wind tunnel at x ¼ 0 and 7.08 km, respectively. Almost coincident profiles near the surface are obtained between field observations and wind tunnel experiments.
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Fig. 6. Wind direction observed around the height of tracer gas release. Open and shaded circles indicate wind directions in field observations at z ¼ 100 and 150 m, respectively. The line indicates wind direction in wind tunnel.
Because of the difficulty in determining the ground surface temperature of the whole field observation area, temperature was normalized using the values measured nearest the ground surface, viz., Tw ; equivalent observed heights were about 1 and 6 m from the ground surface for atmosphere and the wind tunnel, respectively. The results are shown in Fig. 7. With the normalization of temperature applied, temperature variations with height are enlarged and it is straightforward to compare the profiles between the wind tunnel and field observations. Temperature profiles obtained from field observations were also average values of several observations made during the tracer gas releases. Temperature profiles in Fig. 7 correspond to the five cases in which the three similarity criteria described in Section 3.2 were satisfied. An unstable temperature gradient was observed for both atmosphere and the wind tunnel near the ground surface. Temperature profiles of the wind tunnel showed good agreement with those of atmosphere near the coastline, viz., Point 3 and x ¼ 2:5 km for atmosphere and the wind tunnel, respectively. On increasing distance from the coastline, viz., at Point 5 in atmosphere, the temperature increased near the ground in some cases, viz., runs 4 and 6. This was due to active turbulent mixing near the ground surface, and vertically uniform temperature profiles tended to be enhanced. On increasing the distance from the coastline, viz., at x ¼ 7:08 km in the wind tunnel, the thickness of the thermal boundary layer was enlarged and the regions with an unstable temperature gradient reached almost several hundred meters from the ground. On the other hand, in
Fig. 7. Temperature in field observations and wind tunnel. The solid lines with open and shaded circles correspond to field observations at Point 3 and Point 5, respectively. The bold line and bold dotted line correspond to wind tunnel at x ¼ 2:5 and 7.08 km, respectively. Almost coincident values near the surface are obtained for wind tunnel experiments at x ¼ 2:5 and 7.08 km, and closer to field observations.
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atmosphere, because weak stable temperature gradients were observed at elevated positions, increase of the thickness of the thermal boundary layer was suppressed. Consequently, some discrepancies arose at elevated positions. However, such discrepancies were limited to elevated positions; almost the same temperature profiles were obtained at regions near the ground at an inland area. 4.3. Ground level concentration measurement and comparison with field experiment The ground level concentration of tracer gas, normalized by the source strength and representative wind velocity, is shown in Fig. 8 together with those of field observations. Ground level concentrations in Fig. 8 correspond to the five cases in which the three similarity criteria described in Section 3.2 were satisfied. Maximum values of ground level concentration at each sampling arc, viz., not the sampling points located west of the point of tracer gas release, were used as field observation data. However, maximum values were observed at sampling points located nearly perpendicular to the coastline. Ground level concentration obtained from wind tunnel experiments showed the maximum
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value at around x ¼ 2:5 km, and smoothly varied with distance from the tracer gas point of release. On the other hand, because ground level concentrations in field observations were obtained at discrete sampling points and were affected by the variation of meteorological conditions, viz., wind velocity and wind direction, scatter was observed in the data. However, ground level concentrations observed in the field were distributed around that obtained in the wind tunnel, and disagreement from the wind tunnel value was not large. The maximum ground level concentration and the observed distance in the field were normalized with those in the wind tunnel, considering a length scale ratio of 1200, and are indicated in Fig. 9. Normalized concentrations were larger than unity and normalized distances were less than unity when the three similarity criteria were not satisfied. In such cases, released tracer gas tended to reach the ground surface more rapidly, and concentrations tended to increase compared with those in the wind tunnel. However, normalized concentrations and distances were around unity when the three similarity criteria were satisfied. This was due to the fact that the ground level concentrations obtained in field observations were well simulated by the wind tunnel when similarity criteria were satisfied.
Fig. 8. Normalized ground level concentration with source strength and representative velocity for field observations and wind tunnel. The solid line and the circles correspond to wind tunnel and field observations, respectively.
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observations were well simulated in the wind tunnel when the three similarity criteria were satisfied.
References
Fig. 9. Maximum ground level concentration and its location in field observations normalized with those in wind tunnel. The open and shaded circles indicate cases when three similarity criteria are satisfied and not satisfied, respectively.
5. Conclusions In the present study, wind tunnel experiments under unstable conditions were conducted by heating the wind tunnel floor to simulate tracer gas diffusion over a coastal region. Three similarity criteria were used to define the unstable stratification condition in the wind tunnel. Consequently, five cases of field experiment data sets were inferred to indicate almost the same stratification condition as in the wind tunnel, and four remaining cases were inferred to be more unstable than that in the wind tunnel. Then, wind tunnel experiment results were compared with those of a field experiment conducted at Tokai village in 1982. The profiles of mean wind velocity and temperature obtained in the wind tunnel showed good agreement with those in atmosphere when the three similarity criteria were satisfied. Furthermore, it was revealed that maximum values of the ground level concentration and its observed distance from the position of tracer gas release obtained in field
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