Concentration Prediction Equations

The previous example showed a snapshot of the particle or puff center positions after 12 hours.  Air concentrations are computed by summing each particle’s mass as it passes over the concentration grid.  In the particle model mode, the concentration grid is treated as a matrix of cells, each with a volume defined by the grid dimensions.  Therefore the concentration is just the particle mass divided by the cell volume.

     3D Particle:      ΔC = q(Δx Δy Δz)^-1
     Top-Hat:           ΔC = q(Π r² Δz)^-1
     Guassian:        ΔC = q(2Π σ_h² Δz)^-1 e^{- 0.5x2/σh2}

In the puff calculation, the concentration grid is considered as a matrix of sampling points, such that the puff only contributes to the concentration as it passes over the sampling point.  In the puff calculation mode it is possible for a puff to pass between points and not be shown on the display.

     Top-Hat:           ΔC = q(Π r² Δz_p)^-1
     Guassian:        ΔC = q(2Π σ_h² Δz_p)^-1 e^{- 0.5x2/σh2}

Shown below are the concentration patterns associated with the particle (left) and puff (right) distributions from the previous example.  Note that the puff distribution is smoother but also initially somewhat broader.  In this particular case, the horizontal puff growth equations give larger values than the particle expansion. The noisy particle distribution indicates that more particles than 5000 are needed to better represent the horizontal distribution.

Particle Concentrations

Top-Hat Puff Concentrations