ENAC-SSIE Laboratoire de Pollution de l'Air Model Strategies Simplify the equations Find an analytical solution Keep the equations Simplify the resolution.

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Presentation transcript:

ENAC-SSIE Laboratoire de Pollution de l'Air Model Strategies Simplify the equations Find an analytical solution Keep the equations Simplify the resolution

ENAC-SSIE Laboratoire de Pollution de l'Air Gaussian Model Wind speed Virtual Source Non reactive Pollutant Punctual Pollutant Source Constant Wind Homogenous Turbulence

ENAC-SSIE Laboratoire de Pollution de l'Air Gaussian Model with C pollutant concentration [gm -3 ], Q pollutant fluxes at the source [gs -1 ], U mean wind speed [ms -1 ],  y  standard deviation of the horizontal turbulent distribution [m],  z  standard deviation of the vertical turbulent distribution [m], H effective height of the pollutant source [m].

ENAC-SSIE Laboratoire de Pollution de l'Air Gaussian Model Pasquill classes for atmospheric stability

ENAC-SSIE Laboratoire de Pollution de l'Air Gaussian Model StabilityParameters (x in km) A T = – ln x B C D E F T = – ln x T = 12.5 – ln x T = – ln x T = 6.25 – ln x T = – ln x withx the distance to the pollutant source [km]

ENAC-SSIE Laboratoire de Pollution de l'Air Gaussian Model with x the distance to the pollutant source [km]

ENAC-SSIE Laboratoire de Pollution de l'Air Lagrangian Particles Model Concentration U  x=U  t  x=(U+u)  t U u Air parcel trajectories Additional turbulent wind speed

ENAC-SSIE Laboratoire de Pollution de l'Air Box Model Eulerian: fixed box Wind flow Lagrangian: moving box Wind flow: Box trajectory

ENAC-SSIE Laboratoire de Pollution de l'Air Moving column Wind flow: Column trajectory Lagrangian Column Model

ENAC-SSIE Laboratoire de Pollution de l'Air Eulerian 3D Model Eulerian 3D mesh

ENAC-SSIE Laboratoire de Pollution de l'Air Eulerian 3D Model xx i-1 i i+1 C 2/1i F  n i C 2/1i F  i S

ENAC-SSIE Laboratoire de Pollution de l'Air xx i-1 i i+1 n i C Eulerian 3D Model tt Time Distance n+1 i C Boundary Conditions B.C. Initial Conditions

ENAC-SSIE Laboratoire de Pollution de l'Air Eulerian 3D Model Exact solution after 5s Initial condition Exact solution

ENAC-SSIE Laboratoire de Pollution de l'Air Eulerian 3D Model with

ENAC-SSIE Laboratoire de Pollution de l'Air Initial condition Solution after 5s  t=0.5s  t=0.1s Eulerian 3D Model 1 st order and

ENAC-SSIE Laboratoire de Pollution de l'Air Eulerian 3D Model

ENAC-SSIE Laboratoire de Pollution de l'Air Eulerian 3D Model 1 st and 3 d order and 1 st order 3 d order Initial condition