- Email: [email protected]
Gas diffusion in a convection layer near a coastal region
Journal of Wind Engineering and Industrial Aerodynamics 81 (1999) 171}180
Gas di!usion in a convection layer near a coastal region Akinori Kouchi *, Ryoji Ohba , Yanping Shao Nagasaki Research & Development Center, Fluid Dynamics Laboratory, Mitsubishi Heavy Industries, LTD., Nagasaki 851-0392, Japan Center for Advanced Numerical Computation in Engineering and Science, University of New South Wales, Sydney, Australia
Abstract Thermal internal boundary layer (TIBL) in onshore wind has a signi"cant in#uence on dispersion of air pollutants and causes fumigation which brings high ground level concentration (GLC) of pollutants. A wind tunnel experiment was conducted in the thermally strati"ed wind tunnel of Nagasaki Research & Development Center, MHI, Japan, for the purpose of investigating the e!ect of TIBL on GLC and turbulent statistical properties. Numerical simulations using a Lagrangian stochastic dispersion model were also conducted and its results were compared with wind tunnel results and "led observation. Concerning GLC, they showed good agreement and this con"rms the usefulness of a Lagrangian stochastic model in practical application to predict GLC in coastal areas. 1999 Elsevier Science Ltd. All rights reserved. Keywords: TIBL; Fumigation; Lagrangian stochastic dispersion model; Wind tunnel experiment
1. Introduction In coastal onshore air #ows, a thermal internal boundary layer (TIBL) often develops as a result of abrupt change in temperature between sea surface and land surface. In TIBL, turbulent properties are considerably di!erent from those of stable or neutral boundary layers, and these di!erences have a signi"cant in#uence on dispersion of air pollutants in the coastal area, and causes the fumigation phenomenon which brings high ground level concentration (GLC) as shown in Fig. 1 [1}3].
* Corresponding author. Tel.: #81-95-834-2832; fax: #81-95-834-2385. E-mail address: [email protected] (A. Kouchi) 0167-6105/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 9 ) 0 0 0 1 5 - X
172
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
Fig. 1. Schematic diagram of TIBL fumigation.
In this paper, we describe a wind tunnel experiment conducted in the thermally strati"ed wind tunnel in Nagasaki Research & Development Center, MHI, Japan for the purpose of investigating the e!ect of TIBL on GLCs and turbulent statistical properties. The GLCs obtained by wind tunnel experiment were compared with "eld observations carried out in Tokai area, Japan, 1984 [4]. Both the GLCs agree well with each other and it indicates the validity of the wind tunnel experiment. On the other hand, numerical calculation simulating the same condition as wind tunnel experiment was also mentioned. The numerical model used in this simulation is the Lagrangian stochastic model which was originally developed by the Center for Advanced Numerical Computation in Engineering and Science (CANCES), University of New South Wales, Australia. This model is able to predict GLCs taking account of TIBL e!ect on turbulent dispersion both in stable layer (homogeneous turbulence) and unstable convective layer (inhomogeneous turbulence). The wellmixed condition and Kolmogorov's local similarity theory are applied to determine the advection and di!usion coe$cients in the model. The turbulent parameters required in the model such as velocity variance, skewness, and dissipation rate of turbulent kinetic energy are determined by the similarity theory of the convective layer based on airbone observations. This study provides quantitative comparisons between these results.
2. Wind tunnel experiment 2.1. Experimental facilities The con"guration of the thermally strati"ed wind tunnel is illustrated in Fig. 2. This suction-type wind tunnel has a test section with 15.5 m length, 2.5 m width and 1.0 m
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
173
Fig. 2. Schematic of wind tunnel experiment in the thermally strati"ed wind tunnel.
height. A space-heating unit is placed upstream of the test section. This unit is horizontally divided into 10 layers and each layer has an electric heater and the temperature of air #ow passing in each layer can be controlled separately to generate continuous temperature strati"cation. The #oor of the wind tunnel is also divided into several panels and the temperature of each panel can be controlled independently by using an electrical #oor heating unit and #oor cooling unit. In the wind tunnel experiments simulating coastal TIBL, the air #ow is stably strati"ed by the spaceheating unit and a #oor panel corresponding to the sea surface was cooled to simulate a stable layer, and then the #oor panel corresponding to the land surface was heated to generate the unstable convective boundary layer. The velocity components of the #ow are measured with a "ber laser velocimeter (FLV), Nihon Kagaku Kougyo, Japan. The measurements are taken at various X (downwind distance) and Z (height) in the center of the test section. Flow temperature is also measured with a platinum resistance sensor (cold-wire). The sampling rate for temperature measurements is 100 Hz. Methane gas (CH ) is used as tracer gas and released from a !-shape stack model as a point source which simulates the stack of the power plant or chemical plant near the coast. To investigate the ground level concentration, arrays of sampling tubes are mounted on the wind tunnel #oor, from which air samples are taken. The samples are later analyzed in the laboratory using a Hydro Carbon gas analyzer (Shimazu, Japan). Air samples are also taken from a mobile sampling tube at di!erent places in the air #ow, and from these samples the tracer gas concentrations are analyzed using a fast response hydrocarbon meter, HFR-400 (Cambustion, UK). 2.2. Experimental method The similarity rule of bulk Richardson number, Ri was applied to determine the wind tunnel #ow speed and temperature di!erence between cooling panel and heating
174
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180 Table 1 Experimental parameters Case
Case Case Case Case Case
1 2 3 4 5
x (m)
z (m)
;
(m/s)
*¹ (K)
H (W/m)
c (K/m)
!1000 !1000 100 100 100
200 50 200 50 120
6 6 6 6 6
4.5 4.5 4.5 4.5 4.5
350 350 350 350 350
0.0075 0.0075 0.0075 0.0075 0.0075
x is the onshore distance of the source from coastline, z is the source height, ; the mean #ow speed, H the surface heat #ux and c the temperature gradient in
the stable layer. Parameters are given in equivalent "eld scale values.
panel. The bulk Richardson number is de"ned by the following equation, g¸*¹ Ri " , ;¹
(1)
where g is the gravity acceleration, ¸ is the reference length (chosen as the height of the pollutant souse), ; is the wind speed and *¹ is the temperature di!erence between two #oor panels. The detailed reason for using the bulk Richardson number as the similarity rule in non-neutral atmospheric #ows has been discussed by Ohba et al. [5]. In this study, "ve case experiments were carried out as summarized in Table 1. The results were compared with results of numerical calculations using the Lagrangian stochastic dispersion model described later, and especially with regard to Case 5, its result was also compared with "eld observation carried out in the Tokai area, Japan, 1984 [4]. The parameters in Table 1 are converted from corresponding model-scaled values in the wind tunnel. The spatial scaling between wind tunnel and "eld observation (Case 5 corresponds to Tokai area "eld observation) is 1/2000. In this scaling, according to the bulk Richardson number similarity theory, a #ow speed of 0.42 m/s in the wind tunnel corresponds to 6 m/s in "eld scale, and a temperature di!erence of 45 K corresponds 4.5 K in "eld scale.
3. Numerical simulation 3.1. Lagrangian stochastic dispersion model The Lagrangian stochastic dispersion model [6] used in this paper was originally developed by the Center for Advanced Numerical Computation in Engineering and Science (CANCES), University of New South Wales, Australia, and applied to our simulation.
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
175
Based on the Lagrangian stochastic model, the movement of a passive particle in a turbulent #ow is described by the equation system below, d; "a dt#(C e dm , G G G
(2)
dX "; dt , G G
(3)
where ; and X are the velocity and position of the particle, respectively, t is the time G G and dm is a random acceleration, C is the Kolmogorov constant, and e is the G dissipation rate for turbulent kinetic energy. The drift coe$cient a is determined by G solving the Fokker}Planck equation assuming the well-mixed condition [7]. To apply the Lagrangian stochastic model to coastal areas, the probability density function of Eulerian velocity #uctuations, P , needs to be speci"ed. It is assumed in this study that # the velocity components are uncorrelated i.e. P (u, v, w)"P (u)P (v)P (w). # # # #
(4)
. In this study, for the stable region of the coastal atmospheric boundary layer, P of # each velocity component is assumed to have Gaussian distribution. On the other hand, within the TIBL region, P of u and v components are assumed to be Gaussian # but no longer Gaussian for the case of w component because of in#uence of convection. Instead of normal Gaussian distribution, P of w component in TIBL is modeled # using a combination of bi-Gaussian distributions, namely updraft component and downdraft component [8]. To determine the parameters in the Gaussian or bi-Gaussian distribution, turbulent properties including variances and skewness of turbulent #uctuations and the dissipation rate of turbulent kinetic energy are required. For the stable region of the coastal boundary layer, the variance of velocity components as well as the dissipation rate for turbulent kinetic energy can be assumed to be constant and skewness is zero. In the numerical simulation presented later, these turbulence variables are speci"ed according to the wind tunnel observations. For the convective region of the coastal boundary layer, turbulence properties vary in space. Following Shao et al. [9] the turbulent quantities required by the Lagrangian stochastic model can be expressed as functions depending on z/z , when properly G scaled by convective scaling velocity w [10], where z is the TIBL depth. The scaling HV G velocity and z [11] are expressed as G
(5)
2H x z" , G oC c;
(6)
g H z , w " G HV ¹ oC
where o is the air density and C is the speci"c heat of the atmosphere. H is assumed N independent of the onshore distance.
176
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
The similarity relationships relevant to the present study are expressed as follows:
z z p "(2w 1!0.8 , U HV z z G G z S "0.42 1! I z G
1!0.8
z \ , z G
1 z w HV, e" 1.3#0.1 z z (8 G G
(7)
(8)
(9)
where p and S are the standard deviation and skewness of the vertical velocity U I component, respectively.
4. Results 4.1. Properties of TIBL Fig. 3 is a comparison of p normalized with w between the wind tunnel U HV observations and the "eld observations [9]. The solid line in Fig. 3 represents Eq. (7) used in the numerical model. They show good agreement and this means that the assumptions of similarity relationships used in the model are valid. Fig. 4 also shows the comparison of TIBL height between the model (Eq. (6)), wind tunnel measurement and "eld observation of Tokai area. As can be seen, Eq. (6) "ts well the observed data and it indicates the reasonableness of the approximation using Eq. (6).
Fig. 3. Comparison of turbulent intensity.
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
177
Fig. 4. Comparison of TIBL depth.
Table 2 Summary of parameters used in the numerical simulation. The velocity variance and dissipation rate of turbulent kinetic energy were e measured in the stable region of the wind tunnel #ow H (W/m)
c (K/m)
;
(m/s)
p S (m/s)
p T (m/s)
p U (m/s)
e (m/s)
350
0.0075
6
0.25
0.25
0.25
0.001
Fig. 5. Contour of concentration in the vertical cross section.
4.2. Concentration of pollutant Ground level concentration (GLC) is the major concern for practical environmental assessment. In this section, comparisons of axial GLC are shown. The parameters used in the numerical simulation are estimated from the wind tunnel measurements, as summarized in Table 2. The turbulence statistics in Table 2 are measured for the stable region of the coastal boundary layer, while for the convective region, the turbulence properties are speci"ed according to the similarity laws described in the previous section.
178
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
Fig. 6. Comparison of axial GLC. X-axis means the downwind distance from the source normalized with the source height z , >-axis means axial GLC normalized with ;, z and source strength Q. (a) Case 1 (Z "200 m, X "!1000 m). (b) Case 2 (Z "50 m, X "!1000 m). (c) Case 3 (Z "200 m, X "100 m). (d) Case 4 (Z "50 m, X "100 m). (e) Case 5 (Z "120 m, X "100 m).
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
179
Numerical simulations for the "ve cases shown in Table 1 were carried out and compared with the wind tunnel observations. Fig. 5 gives a calculated result of the X}Z cross-section of concentration contours. The basic features of the simulated concentration "elds are as expected. In the stable region of the coastal boundary layer, the distribution and transport of the air pollutant are relatively small and show typical characteristics of Gaussian plumes. Here, the concentration is maximal at the source height. On the other hand in the convective region of the boundary layer, particles are rapidly dispersed to lower layers, increasing the ground level concentration. Comparison of axial GLC between the numerical simulation, the wind tunnel experiments and "eld observation (for Case 5 only) is shown in Fig. 6. The overall agreement between the numerical simulation and the wind tunnel observations is very good. In Case 5, comparison with "eld observation is given and the agreement is good. The best agreement appears in Cases 1 and 3, for which the source height is 200 m. The worst agreement is Case 4, for which the source height is 50 m. For this case, maximum GLC is at a smaller distance than observed. Possible reason of this discrepancy is as follows. In the numerical model, turbulence properties are determined according to the similarity theory of the convective layer, and therefore may not properly describe the features of turbulence near the surface. In this case, the discrepancy between wind tunnel measurements and numerical model results will be the most obvious.
5. Conclusions In this study, numerical simulation and wind tunnel experiments are conducted for the purpose of investigating fumigation in coastal atmospheric boundary layers. Lagrangian stochastic dispersion model was applied to this problem and its results were compared with wind tunnel results and "led observation. As far as the axial ground level concentration is concerned, they showed good agreement and this con"rms the usefulness of the Lagrangian stochastic model in practical applications to predict GLC in coastal areas.
References [1] W.A. Lyons, H.S. Cole, Fumigation and plume trapping on the shores of Lake Michigan during stable onshore #ow, J. Appl. Meteorol. 12 (1973) 495}510. [2] P.K. Mirsa, Dispersion from tall stacks into a shoreline environment, Atmos. Environ. 14 (1980) 396}400. [3] A. Luhar, B.L. Sawford, An examination of existing shoreline fumigation models and formulation of an improved model, Atmos. Environ. 30 (1995) 609}620. [4] M. Kakuta, T. Hayashi, Results of atmospheric di!usion experiments, vol. 2 TOKAI82, TOKAI83, JAERI-M 86-097, vol. 2, 1986. [5] R. Ohba, S. Kakishima, S. Ito, Water tank experiment of gas di!usion from a stack in stably and unstably strati"ed layers under calm conditions, Atmos. Environ. 25 (1991) 2063}2076.
180
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
[6] Y. Shao, Turbulent dispersion in coastal atmospheric boundary layers: an application of Lagrangian model, Boundary-Layer Meteorol. 59 (1992) 363}385. [7] D.J. Thomson, Criteria for the selection of stochastic models of particle trajectries in turbulent #ows, J. Fluid Mech. 180 (1987) 529}556. [8] J.H. Baerentsen, Z. Berkowicz, Monte Carlo simulation of plume dispersion in the convective boundary layer, Atmos. Environ. 18 (1984) 701}712. [9] Y. Shao, J.M. Hacker, P. Schwerdtfeger, The structure of turbulence in a coastal atmospheric boundary layer, Quart. J. Roy. Meteorol. Soc. 117 (1991) 1299}1324. [10] J.W. Deardor!, G.E. Willis, Ground-level concentrations due to fumigation into an entraining mixed layer, Atmos. Environ. 16 (1982) 1159}1170. [11] B. Weisman, On the criteria for the occurrence of fumigation inland from a large lake } a reply, Atmos. Environ. 12 (1976) 172}173.
Gas di!usion in a convection layer near a coastal region Akinori Kouchi *, Ryoji Ohba , Yanping Shao Nagasaki Research & Development Center, Fluid Dynamics Laboratory, Mitsubishi Heavy Industries, LTD., Nagasaki 851-0392, Japan Center for Advanced Numerical Computation in Engineering and Science, University of New South Wales, Sydney, Australia
Abstract Thermal internal boundary layer (TIBL) in onshore wind has a signi"cant in#uence on dispersion of air pollutants and causes fumigation which brings high ground level concentration (GLC) of pollutants. A wind tunnel experiment was conducted in the thermally strati"ed wind tunnel of Nagasaki Research & Development Center, MHI, Japan, for the purpose of investigating the e!ect of TIBL on GLC and turbulent statistical properties. Numerical simulations using a Lagrangian stochastic dispersion model were also conducted and its results were compared with wind tunnel results and "led observation. Concerning GLC, they showed good agreement and this con"rms the usefulness of a Lagrangian stochastic model in practical application to predict GLC in coastal areas. 1999 Elsevier Science Ltd. All rights reserved. Keywords: TIBL; Fumigation; Lagrangian stochastic dispersion model; Wind tunnel experiment
1. Introduction In coastal onshore air #ows, a thermal internal boundary layer (TIBL) often develops as a result of abrupt change in temperature between sea surface and land surface. In TIBL, turbulent properties are considerably di!erent from those of stable or neutral boundary layers, and these di!erences have a signi"cant in#uence on dispersion of air pollutants in the coastal area, and causes the fumigation phenomenon which brings high ground level concentration (GLC) as shown in Fig. 1 [1}3].
* Corresponding author. Tel.: #81-95-834-2832; fax: #81-95-834-2385. E-mail address: [email protected] (A. Kouchi) 0167-6105/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 9 ) 0 0 0 1 5 - X
172
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
Fig. 1. Schematic diagram of TIBL fumigation.
In this paper, we describe a wind tunnel experiment conducted in the thermally strati"ed wind tunnel in Nagasaki Research & Development Center, MHI, Japan for the purpose of investigating the e!ect of TIBL on GLCs and turbulent statistical properties. The GLCs obtained by wind tunnel experiment were compared with "eld observations carried out in Tokai area, Japan, 1984 [4]. Both the GLCs agree well with each other and it indicates the validity of the wind tunnel experiment. On the other hand, numerical calculation simulating the same condition as wind tunnel experiment was also mentioned. The numerical model used in this simulation is the Lagrangian stochastic model which was originally developed by the Center for Advanced Numerical Computation in Engineering and Science (CANCES), University of New South Wales, Australia. This model is able to predict GLCs taking account of TIBL e!ect on turbulent dispersion both in stable layer (homogeneous turbulence) and unstable convective layer (inhomogeneous turbulence). The wellmixed condition and Kolmogorov's local similarity theory are applied to determine the advection and di!usion coe$cients in the model. The turbulent parameters required in the model such as velocity variance, skewness, and dissipation rate of turbulent kinetic energy are determined by the similarity theory of the convective layer based on airbone observations. This study provides quantitative comparisons between these results.
2. Wind tunnel experiment 2.1. Experimental facilities The con"guration of the thermally strati"ed wind tunnel is illustrated in Fig. 2. This suction-type wind tunnel has a test section with 15.5 m length, 2.5 m width and 1.0 m
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
173
Fig. 2. Schematic of wind tunnel experiment in the thermally strati"ed wind tunnel.
height. A space-heating unit is placed upstream of the test section. This unit is horizontally divided into 10 layers and each layer has an electric heater and the temperature of air #ow passing in each layer can be controlled separately to generate continuous temperature strati"cation. The #oor of the wind tunnel is also divided into several panels and the temperature of each panel can be controlled independently by using an electrical #oor heating unit and #oor cooling unit. In the wind tunnel experiments simulating coastal TIBL, the air #ow is stably strati"ed by the spaceheating unit and a #oor panel corresponding to the sea surface was cooled to simulate a stable layer, and then the #oor panel corresponding to the land surface was heated to generate the unstable convective boundary layer. The velocity components of the #ow are measured with a "ber laser velocimeter (FLV), Nihon Kagaku Kougyo, Japan. The measurements are taken at various X (downwind distance) and Z (height) in the center of the test section. Flow temperature is also measured with a platinum resistance sensor (cold-wire). The sampling rate for temperature measurements is 100 Hz. Methane gas (CH ) is used as tracer gas and released from a !-shape stack model as a point source which simulates the stack of the power plant or chemical plant near the coast. To investigate the ground level concentration, arrays of sampling tubes are mounted on the wind tunnel #oor, from which air samples are taken. The samples are later analyzed in the laboratory using a Hydro Carbon gas analyzer (Shimazu, Japan). Air samples are also taken from a mobile sampling tube at di!erent places in the air #ow, and from these samples the tracer gas concentrations are analyzed using a fast response hydrocarbon meter, HFR-400 (Cambustion, UK). 2.2. Experimental method The similarity rule of bulk Richardson number, Ri was applied to determine the wind tunnel #ow speed and temperature di!erence between cooling panel and heating
174
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180 Table 1 Experimental parameters Case
Case Case Case Case Case
1 2 3 4 5
x (m)
z (m)
;
(m/s)
*¹ (K)
H (W/m)
c (K/m)
!1000 !1000 100 100 100
200 50 200 50 120
6 6 6 6 6
4.5 4.5 4.5 4.5 4.5
350 350 350 350 350
0.0075 0.0075 0.0075 0.0075 0.0075
x is the onshore distance of the source from coastline, z is the source height, ; the mean #ow speed, H the surface heat #ux and c the temperature gradient in
the stable layer. Parameters are given in equivalent "eld scale values.
panel. The bulk Richardson number is de"ned by the following equation, g¸*¹ Ri " , ;¹
(1)
where g is the gravity acceleration, ¸ is the reference length (chosen as the height of the pollutant souse), ; is the wind speed and *¹ is the temperature di!erence between two #oor panels. The detailed reason for using the bulk Richardson number as the similarity rule in non-neutral atmospheric #ows has been discussed by Ohba et al. [5]. In this study, "ve case experiments were carried out as summarized in Table 1. The results were compared with results of numerical calculations using the Lagrangian stochastic dispersion model described later, and especially with regard to Case 5, its result was also compared with "eld observation carried out in the Tokai area, Japan, 1984 [4]. The parameters in Table 1 are converted from corresponding model-scaled values in the wind tunnel. The spatial scaling between wind tunnel and "eld observation (Case 5 corresponds to Tokai area "eld observation) is 1/2000. In this scaling, according to the bulk Richardson number similarity theory, a #ow speed of 0.42 m/s in the wind tunnel corresponds to 6 m/s in "eld scale, and a temperature di!erence of 45 K corresponds 4.5 K in "eld scale.
3. Numerical simulation 3.1. Lagrangian stochastic dispersion model The Lagrangian stochastic dispersion model [6] used in this paper was originally developed by the Center for Advanced Numerical Computation in Engineering and Science (CANCES), University of New South Wales, Australia, and applied to our simulation.
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
175
Based on the Lagrangian stochastic model, the movement of a passive particle in a turbulent #ow is described by the equation system below, d; "a dt#(C e dm , G G G
(2)
dX "; dt , G G
(3)
where ; and X are the velocity and position of the particle, respectively, t is the time G G and dm is a random acceleration, C is the Kolmogorov constant, and e is the G dissipation rate for turbulent kinetic energy. The drift coe$cient a is determined by G solving the Fokker}Planck equation assuming the well-mixed condition [7]. To apply the Lagrangian stochastic model to coastal areas, the probability density function of Eulerian velocity #uctuations, P , needs to be speci"ed. It is assumed in this study that # the velocity components are uncorrelated i.e. P (u, v, w)"P (u)P (v)P (w). # # # #
(4)
. In this study, for the stable region of the coastal atmospheric boundary layer, P of # each velocity component is assumed to have Gaussian distribution. On the other hand, within the TIBL region, P of u and v components are assumed to be Gaussian # but no longer Gaussian for the case of w component because of in#uence of convection. Instead of normal Gaussian distribution, P of w component in TIBL is modeled # using a combination of bi-Gaussian distributions, namely updraft component and downdraft component [8]. To determine the parameters in the Gaussian or bi-Gaussian distribution, turbulent properties including variances and skewness of turbulent #uctuations and the dissipation rate of turbulent kinetic energy are required. For the stable region of the coastal boundary layer, the variance of velocity components as well as the dissipation rate for turbulent kinetic energy can be assumed to be constant and skewness is zero. In the numerical simulation presented later, these turbulence variables are speci"ed according to the wind tunnel observations. For the convective region of the coastal boundary layer, turbulence properties vary in space. Following Shao et al. [9] the turbulent quantities required by the Lagrangian stochastic model can be expressed as functions depending on z/z , when properly G scaled by convective scaling velocity w [10], where z is the TIBL depth. The scaling HV G velocity and z [11] are expressed as G
(5)
2H x z" , G oC c;
(6)
g H z , w " G HV ¹ oC
where o is the air density and C is the speci"c heat of the atmosphere. H is assumed N independent of the onshore distance.
176
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
The similarity relationships relevant to the present study are expressed as follows:
z z p "(2w 1!0.8 , U HV z z G G z S "0.42 1! I z G
1!0.8
z \ , z G
1 z w HV, e" 1.3#0.1 z z (8 G G
(7)
(8)
(9)
where p and S are the standard deviation and skewness of the vertical velocity U I component, respectively.
4. Results 4.1. Properties of TIBL Fig. 3 is a comparison of p normalized with w between the wind tunnel U HV observations and the "eld observations [9]. The solid line in Fig. 3 represents Eq. (7) used in the numerical model. They show good agreement and this means that the assumptions of similarity relationships used in the model are valid. Fig. 4 also shows the comparison of TIBL height between the model (Eq. (6)), wind tunnel measurement and "eld observation of Tokai area. As can be seen, Eq. (6) "ts well the observed data and it indicates the reasonableness of the approximation using Eq. (6).
Fig. 3. Comparison of turbulent intensity.
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
177
Fig. 4. Comparison of TIBL depth.
Table 2 Summary of parameters used in the numerical simulation. The velocity variance and dissipation rate of turbulent kinetic energy were e measured in the stable region of the wind tunnel #ow H (W/m)
c (K/m)
;
(m/s)
p S (m/s)
p T (m/s)
p U (m/s)
e (m/s)
350
0.0075
6
0.25
0.25
0.25
0.001
Fig. 5. Contour of concentration in the vertical cross section.
4.2. Concentration of pollutant Ground level concentration (GLC) is the major concern for practical environmental assessment. In this section, comparisons of axial GLC are shown. The parameters used in the numerical simulation are estimated from the wind tunnel measurements, as summarized in Table 2. The turbulence statistics in Table 2 are measured for the stable region of the coastal boundary layer, while for the convective region, the turbulence properties are speci"ed according to the similarity laws described in the previous section.
178
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
Fig. 6. Comparison of axial GLC. X-axis means the downwind distance from the source normalized with the source height z , >-axis means axial GLC normalized with ;, z and source strength Q. (a) Case 1 (Z "200 m, X "!1000 m). (b) Case 2 (Z "50 m, X "!1000 m). (c) Case 3 (Z "200 m, X "100 m). (d) Case 4 (Z "50 m, X "100 m). (e) Case 5 (Z "120 m, X "100 m).
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
179
Numerical simulations for the "ve cases shown in Table 1 were carried out and compared with the wind tunnel observations. Fig. 5 gives a calculated result of the X}Z cross-section of concentration contours. The basic features of the simulated concentration "elds are as expected. In the stable region of the coastal boundary layer, the distribution and transport of the air pollutant are relatively small and show typical characteristics of Gaussian plumes. Here, the concentration is maximal at the source height. On the other hand in the convective region of the boundary layer, particles are rapidly dispersed to lower layers, increasing the ground level concentration. Comparison of axial GLC between the numerical simulation, the wind tunnel experiments and "eld observation (for Case 5 only) is shown in Fig. 6. The overall agreement between the numerical simulation and the wind tunnel observations is very good. In Case 5, comparison with "eld observation is given and the agreement is good. The best agreement appears in Cases 1 and 3, for which the source height is 200 m. The worst agreement is Case 4, for which the source height is 50 m. For this case, maximum GLC is at a smaller distance than observed. Possible reason of this discrepancy is as follows. In the numerical model, turbulence properties are determined according to the similarity theory of the convective layer, and therefore may not properly describe the features of turbulence near the surface. In this case, the discrepancy between wind tunnel measurements and numerical model results will be the most obvious.
5. Conclusions In this study, numerical simulation and wind tunnel experiments are conducted for the purpose of investigating fumigation in coastal atmospheric boundary layers. Lagrangian stochastic dispersion model was applied to this problem and its results were compared with wind tunnel results and "led observation. As far as the axial ground level concentration is concerned, they showed good agreement and this con"rms the usefulness of the Lagrangian stochastic model in practical applications to predict GLC in coastal areas.
References [1] W.A. Lyons, H.S. Cole, Fumigation and plume trapping on the shores of Lake Michigan during stable onshore #ow, J. Appl. Meteorol. 12 (1973) 495}510. [2] P.K. Mirsa, Dispersion from tall stacks into a shoreline environment, Atmos. Environ. 14 (1980) 396}400. [3] A. Luhar, B.L. Sawford, An examination of existing shoreline fumigation models and formulation of an improved model, Atmos. Environ. 30 (1995) 609}620. [4] M. Kakuta, T. Hayashi, Results of atmospheric di!usion experiments, vol. 2 TOKAI82, TOKAI83, JAERI-M 86-097, vol. 2, 1986. [5] R. Ohba, S. Kakishima, S. Ito, Water tank experiment of gas di!usion from a stack in stably and unstably strati"ed layers under calm conditions, Atmos. Environ. 25 (1991) 2063}2076.
180
A. Kouchi et al. / J. Wind Eng. Ind. Aerodyn. 81 (1999) 171}180
[6] Y. Shao, Turbulent dispersion in coastal atmospheric boundary layers: an application of Lagrangian model, Boundary-Layer Meteorol. 59 (1992) 363}385. [7] D.J. Thomson, Criteria for the selection of stochastic models of particle trajectries in turbulent #ows, J. Fluid Mech. 180 (1987) 529}556. [8] J.H. Baerentsen, Z. Berkowicz, Monte Carlo simulation of plume dispersion in the convective boundary layer, Atmos. Environ. 18 (1984) 701}712. [9] Y. Shao, J.M. Hacker, P. Schwerdtfeger, The structure of turbulence in a coastal atmospheric boundary layer, Quart. J. Roy. Meteorol. Soc. 117 (1991) 1299}1324. [10] J.W. Deardor!, G.E. Willis, Ground-level concentrations due to fumigation into an entraining mixed layer, Atmos. Environ. 16 (1982) 1159}1170. [11] B. Weisman, On the criteria for the occurrence of fumigation inland from a large lake } a reply, Atmos. Environ. 12 (1976) 172}173.