Gaussian Dispersion Model

Gaussian Dispersion Model - 9/13/11 Aerosol &...

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Unformatted text preview: 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 11 What is Dispersion? • Dispersion: The act or process to drive off or scatter in different directions • Key parameters: – Diffusion due to concentration gradient – Mean air motion that transport pollutants downwind – Turbulent velocity fluctuations that disperse pollutants in in all directions 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 22 Plume Dispersion H X Y Z u Q 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 33 Gaussian Dispersion Model x Cu z C D y C D x C D t C z y x ∂ ∂- ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ 2 2 2 2 2 2 At any point downwind the emission C : concentration D : diffusion coefficient u : wind velocity 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 44 Assumptions: • Mass transfer due to bulk motion in the x- direction far outshadows the contribution due to mass diffusion • Continuous emission • Steady state conditions • u is constant • Conservation of mass Q: So, what will the equation be reduced to? x Cu z C D y C D x C D t C z y x ∂ ∂- ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ 2 2 2 2 2 2 ~0 ~0 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 55 2 2 2 2 z C D y C D x C u z y ∂ ∂ + ∂ ∂ + = ∂ ∂ ⇒ + - = x u D z D y x K C z y 4 exp 2 2 General solution (from math handbook) B.C.? ∫∫ = uCdydz Q Constant K to be determined by boundary condition Q : (mass) emission rate 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 66 Point source at ground level Boundaries ∞ →-∞ ∞ → : : y z Hence, the emission rate is ∫ ∫ ∞ ∞ ∞- + - = 2 2 4 exp dydz x u D z D y x Ku Q z y z y D z z D y y = = * , * Variable transformation * 4 * exp * 4 * exp 2 2 ∫ ∫ ∞ ∞- ∞ - - = dy x u y dz x u z D D x Ku Q z y 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 77 +- = x u D z D y D D x Q C z y z y 4 exp 2 2 2 π From standard integral tables, ( 29 a dx x a 2 exp 2 2 π =- ∫ ∞ Compare these two equations, z y D D K Q π 2 = z y D D Q K π 2 = 9/13/11...
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This note was uploaded on 09/11/2011 for the course ENV 6146 taught by Professor Staff during the Spring '11 term at University of Florida.

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Gaussian Dispersion Model - 9/13/11 Aerosol &...

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