Lattice Gas Wind Field Model
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The 19 th IASTED International Conference on Modelling and Simulation 2008 Quebec City, Quebec, Canada
Lattice Gas Simulation of Wind Fields in the Mexico City Metropolitan Area. A. Salcido, A.T. Celada, T. Castro
Instituto de Investigaciones Eléctricas, México
May, 2008
Motivation • Knowledge of the wind field is necessary for the modeling of transport and dispersion of pollutants.
• There are few information about the wind field in the Mexico City Metropolitan Area (MCMA).
In order to contribute to modelling of transport and dispersion of pollutants in the MCMA, we present a square lattice gas technique to define a 2D wind field diagnostic model to simulate the wind field in MCMA.
Lattice Gas Wind Field Model (LGWFM) Nx x Ny sites 3
2
4
8
6
5
1
0
7
Particle speeds 0
Æ Direction 8
1
Æ Directions 0, 2, 4, 6
21/2
Æ Directions 1, 3, 5, 7
Exclusion principle
Equilibrium distribution function
Mass, momentum and energy conservation
nα =
1 1 + e (ε α − μ ) / kT
Lattice Gas Wind Field Model (LGWFM)
1) Reproduction of laminar and turbulent situations such as Couette 2D plane flow.
2) Reproduction the quasi-logarithmic wind velocity vertical profile.
3) Application of LGWFM to simulate the steady state wind field in the Mexico City Metropolitan Area, for daytime and nighttime conditions
Couette Laminar Flow and Logarithmic Wind Velocity Profile 207 x 207 sites U = 0.1, 0.3, 0.5, 0.7 and 0.9
u* ⎡ ⎛ y ⎞ y ⎞⎤ ⎛ u(y) = ⎢ln⎜⎜ ⎟⎟ − ΨM ⎜ ⎟⎥ k ⎣ ⎝ yo ⎠ ⎝ L ⎠⎦ ⎡ y +1 ⎤ ΨM = a ( y − yo) ln ⎢ ⎥ ⎣ b ( y − 1) ⎦ y0 = 10.5 a = 0.2 b = 1.016 u*/k = 0.3
Lattice Gas Wind Field Model (LGWFM) to simulate wind fields in the MCMA
Laticce: 396 x 324 sites Spatial resolution: 180 m July 31 and August 26, 1994 9h
15 h
21 h
Lattice Gas Wind Field Model (LGWFM) to simulate wind fields in the MCMA RAMA
Date: 07/31/94
Local Time: 09:00 Measured
Station
WSP (m/s)
Estimated WDR (°N)
WSP (m/s)
WDR (°N)
IZTACALA
1.00
353
0.95
355
TEXCOCO
1.92
351
1.97
350
UNAM
0.97
5
1.00
3
IZTAPALAPA
0.71
4
0.78
0
TLANEPANTLA
----
----
1.55
313
SN. AGUSTIN
1.70
339
2.88
30
ACATLAN
1.21
300
0.88
305
TACUBA
----
----
0.38
297
HANGARES
1.70
324
2.53
24
C. ESTRELLA
1.21
2
1.08
338
PLATEROS
1.16
352
0.97
21
July 31, 1994,9 hr
July 31, 1994 15 hr
Date: 07/31/94
Local Time: 15:00 Measured
Station
Estimated
WSP (m/s)
WDR (°N)
WSP (m/s)
WDR (°N)
IZTACALA
2.50
354
2. 53
354
TEXCOCO
2.51
339
2.55
340
UNAM
1.33
8
1.34
8
IZTAPALAPA
2.23
47
2.30
47
TLANEPANTLA
----
----
4.13
318
SN. AGUSTIN
2.59
347
4.40
25
ACATLAN
3.53
32
2.19
334
TACUBA
----
----
2.16
326
HANGARES
4.10
15
3.30
14
C. ESTRELLA
2.28
26
1.79
348
PLATEROS
2.37
352
1.24
31
July 31, 1994 21 hr
Date: 07/31/94
Local Time: 21:00 Measured
Estimated
Station
WSP (m/s)
WDR (°N)
WSP (m/s)
WDR (°N)
IZTACALA
1.24
356
1.30
356
TEXCOCO
1.35
355
1.36
355
UNAM
0.45
25
0.49
24
IZTAPALAPA
1.79
71
1.83
70
TLANEPANTLA
----
----
4.13
318
SN. AGUSTIN
2.55
6
2.34
33
ACATLAN
3.40
200
1.52
170
TACUBA
----
----
1.23
153
HANGARES
2.41
216
2.00
40
C. ESTRELLA
1.88
341
0.43
9
PLATEROS
2.41
311
1.00
45
CONCLUSIONS • It is used a lattice gas techniques as an alternative approach to the wind field diagnostic problem, in 2D.
• The computer simulations to test the model showed off that it is capable to reproduce steady and non steady laminar and turbulent well known flow situations. In particular, it was capable to reproduce the typical surface layer quasi-logarithmic wind profile.
• Although the model is still in the validation and calibration phase, it was possible to estimate the wind field of the Mexico City Metropolitan Area with a reasonable agreement with the wind data measured at the meteorological stations of the automatic monitoring network of Mexico City.
Lattice Gas Simulation of Wind Fields in the Mexico City Metropolitan Area. A. Salcido, A.T. Celada, T. Castro
Instituto de Investigaciones Eléctricas, México
May, 2008
Motivation • Knowledge of the wind field is necessary for the modeling of transport and dispersion of pollutants.
• There are few information about the wind field in the Mexico City Metropolitan Area (MCMA).
In order to contribute to modelling of transport and dispersion of pollutants in the MCMA, we present a square lattice gas technique to define a 2D wind field diagnostic model to simulate the wind field in MCMA.
Lattice Gas Wind Field Model (LGWFM) Nx x Ny sites 3
2
4
8
6
5
1
0
7
Particle speeds 0
Æ Direction 8
1
Æ Directions 0, 2, 4, 6
21/2
Æ Directions 1, 3, 5, 7
Exclusion principle
Equilibrium distribution function
Mass, momentum and energy conservation
nα =
1 1 + e (ε α − μ ) / kT
Lattice Gas Wind Field Model (LGWFM)
1) Reproduction of laminar and turbulent situations such as Couette 2D plane flow.
2) Reproduction the quasi-logarithmic wind velocity vertical profile.
3) Application of LGWFM to simulate the steady state wind field in the Mexico City Metropolitan Area, for daytime and nighttime conditions
Couette Laminar Flow and Logarithmic Wind Velocity Profile 207 x 207 sites U = 0.1, 0.3, 0.5, 0.7 and 0.9
u* ⎡ ⎛ y ⎞ y ⎞⎤ ⎛ u(y) = ⎢ln⎜⎜ ⎟⎟ − ΨM ⎜ ⎟⎥ k ⎣ ⎝ yo ⎠ ⎝ L ⎠⎦ ⎡ y +1 ⎤ ΨM = a ( y − yo) ln ⎢ ⎥ ⎣ b ( y − 1) ⎦ y0 = 10.5 a = 0.2 b = 1.016 u*/k = 0.3
Lattice Gas Wind Field Model (LGWFM) to simulate wind fields in the MCMA
Laticce: 396 x 324 sites Spatial resolution: 180 m July 31 and August 26, 1994 9h
15 h
21 h
Lattice Gas Wind Field Model (LGWFM) to simulate wind fields in the MCMA RAMA
Date: 07/31/94
Local Time: 09:00 Measured
Station
WSP (m/s)
Estimated WDR (°N)
WSP (m/s)
WDR (°N)
IZTACALA
1.00
353
0.95
355
TEXCOCO
1.92
351
1.97
350
UNAM
0.97
5
1.00
3
IZTAPALAPA
0.71
4
0.78
0
TLANEPANTLA
----
----
1.55
313
SN. AGUSTIN
1.70
339
2.88
30
ACATLAN
1.21
300
0.88
305
TACUBA
----
----
0.38
297
HANGARES
1.70
324
2.53
24
C. ESTRELLA
1.21
2
1.08
338
PLATEROS
1.16
352
0.97
21
July 31, 1994,9 hr
July 31, 1994 15 hr
Date: 07/31/94
Local Time: 15:00 Measured
Station
Estimated
WSP (m/s)
WDR (°N)
WSP (m/s)
WDR (°N)
IZTACALA
2.50
354
2. 53
354
TEXCOCO
2.51
339
2.55
340
UNAM
1.33
8
1.34
8
IZTAPALAPA
2.23
47
2.30
47
TLANEPANTLA
----
----
4.13
318
SN. AGUSTIN
2.59
347
4.40
25
ACATLAN
3.53
32
2.19
334
TACUBA
----
----
2.16
326
HANGARES
4.10
15
3.30
14
C. ESTRELLA
2.28
26
1.79
348
PLATEROS
2.37
352
1.24
31
July 31, 1994 21 hr
Date: 07/31/94
Local Time: 21:00 Measured
Estimated
Station
WSP (m/s)
WDR (°N)
WSP (m/s)
WDR (°N)
IZTACALA
1.24
356
1.30
356
TEXCOCO
1.35
355
1.36
355
UNAM
0.45
25
0.49
24
IZTAPALAPA
1.79
71
1.83
70
TLANEPANTLA
----
----
4.13
318
SN. AGUSTIN
2.55
6
2.34
33
ACATLAN
3.40
200
1.52
170
TACUBA
----
----
1.23
153
HANGARES
2.41
216
2.00
40
C. ESTRELLA
1.88
341
0.43
9
PLATEROS
2.41
311
1.00
45
CONCLUSIONS • It is used a lattice gas techniques as an alternative approach to the wind field diagnostic problem, in 2D.
• The computer simulations to test the model showed off that it is capable to reproduce steady and non steady laminar and turbulent well known flow situations. In particular, it was capable to reproduce the typical surface layer quasi-logarithmic wind profile.
• Although the model is still in the validation and calibration phase, it was possible to estimate the wind field of the Mexico City Metropolitan Area with a reasonable agreement with the wind data measured at the meteorological stations of the automatic monitoring network of Mexico City.
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