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Understanding the USEPA’s AERMOD Modeling System for Environmental Managers

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Ashok Kumar

Kanwar Siddharth Bhardwaj

Abhilash Vijayan

University of Toledo

Concentration Calculation

- AMBIENT AIR CONCENTRATION MODELING
- Types of Pollutant Sources
- Point Sources e.g., stacks or vents
- Area Sources e.g., landfills, ponds, storage piles
- Volume Sources e.g., conveyors, structures with multiple vents

- Factors Affecting Dispersion of Pollutants in the Atmosphere
- Source Characteristics
- Emission rate of pollutant
- Stack height
- Exit velocity of the gas
- Exit temperature of the gas
- Stack diameter

- Meteorological Conditions
- Wind velocity
- Wind direction
- Ambient temperature
- Atmospheric stability

- Source Characteristics

- Types of Pollutant Sources

- Plume rise calculations
- Concentration calculations
- Dispersion coefficients
- Downwash conditions
- Evaluation

BASIC SEGMENTS OF AN ELEVATED PLUME

- BASIC SEGMENTS OF AN ELEVATED PLUME
- INITIAL PHASE
- Vertical Jet : Effluents are not deflected immediately upon entering the cross flow if (Vs / U > 4 )
- Bent-Over Jet Section : Entrainment of the cross flow is rapid because by this time appreciable growth of vortices has taken place
- Thermal Section : Self generated turbulence causes mixing and determines the growth of plume

- TRANSITION PHASE
- Plume's internal turbulence levels have dropped enough so that the atmospheric eddies in the inertial sub range determines the plume's growth

- DIFFUSION PHASE
- The plume's own turbulence has dropped and energy containing eddies of atmospheric turbulence determine the growth of plume

- TYPES Of PLUME
- Continuos Plume: The release and the sampling time are long compared with the travel time
- Puff Diffusion / Instantaneous Plume: The release time or sampling time is short when compared with the travel time

- TYPES OF PLUME RISE
- Buoyancy Effect: Rise due to the temperature difference between stack plume and ambient air
- Momentum Rise: Rise due to exit velocity of the effluents (emissions)

- CLASSICAL GAUSSIAN PLUME MODELS
- Advantages
- Produce results that match closely with experimental data
- Incorporate turbulence in an ad-hoc manner
- Simple in their mathematics
- Quicker than numerical models
- Do not require super computers

- Disadvantages
- Not suitable if the pollutant is reactive in nature
- Fails to incorporate turbulence in comprehensive sense
- Unable to predict concentrations beyond radius of approximately 20 Km
- For greater distances, wind variations, mixing depths and temporal variations become predominant

- Advantages

SOURCES OF ERROR IN A CLASSICAL GAUSSIAN MODEL

- METHODS TO INCORPORATE PLUME RISE
- The effective Source Height Method
- The variable Plume Model Method

- EFFECTIVE SOURCE HEIGHT METHOD
- Independent of downwind distance, x
- Effective source height.(Screen model)

- h = hs + Dh - ht
- where,
- hs = Physical chimney height
- ht = Maximum terrain height between the source and receptor
- VARIABLE PLUME METHOD
- Takes into account the tilt of the plume

- PLUME DISPERSION PARAMETERS
- Release Height
- Terrain Features
- Velocity Field
- Sampling Time

- No penetration
- Complete penetration
- Partial penetration

- Buoyant Flux
- Momentum Flux
- Brunt-Vaisala Frequency
- Penetration Parameter

Up and N are evaluated initially at stack height and subsequent plume estimates are made iteratively by averaging them at stack top with those at hs+ Δhs/2

FINAL STABLE PLUME RISE EQUATION

- Source can be characterized as point, area, volume.
- Additional ability to account for irregular shaped areas
- Point Source: similar to ISC3
Input: Location, Elevation, Emission rate, Stack height, Stack inside diameter, Stack gas exit velocity, and Temperature.

- Area Source:
- Treatment is enhanced from that available in ISC3
- Input as squares, rectangles, circles or polygons
- Polygons may be defined upto 20 vertices.

- Volume Sources:
- Differs from ISC3 in considering the initial plume size
- Input includes Location, Elevation height, Height of release, Emission rate, Initial lateral and vertical plume rise
- Unlike ISC3, AERMOD adds the square of the initial plume size to the square of ambient plume size
σy2 = σyl2 + σyo2

- Concentration, C is given by the equation
Where,

Q Emission rate

U Effective wind speed

Pypdf in lateral direction

Pzpdf in vertical direction

- AERMOD assumesa traditional Gaussian p.d.f. for both the lateral and vertical distributions in the SBL and for the lateral distribution in the CBL.
- The CBL’s vertical distribution of plume material reflects the distinctly non-Gaussian nature of the vertical velocity distribution in convectively mixed layers.
- Weighting of the 2 states depends on the
- Degree of atmospheric stability
- Wind speed
- Plume height relative to terrain

- Under stable conditions horizontal plume dominates thus given greater weight, while in unstable and neutral conditions terrain rising plume is weighted more.

- In stable flows a stable two layer structure is used: lower layer remains horizontal while upper layer tends to rise over terrain
- Layers are distinguished by the dividing stream line Hc. Plume below the Hc remains horizontal and the plume above Hc follows the hill and rises.
- In neutral and unstable cases lower layer disappears and entire flow rises up the hill.

The total concentration predicted by AERMOD is the weighted sum of the two extreme possible plume states

- The concentrations on a hill lies between values associated with two possible extreme states of a plume:
- Case 1:A horizontal plume that occurs under stable conditions where he flow is forced to go around the hill
- Case 2: Terrain flowing state where the plume rises over terrain
Note: For simple terrain the two cases are equivalent.

Where:

CT {xr, yr, zr} Total Concentration

Cc,s {xr, yr, zr} Concentration from the horizontal plume state

Cc,s {xr, yr, zp}Concentration from the terrain following plume state

fPlume state weighting function

zpHeight of receptor above terrain

zr Elevation of receptor above stack base

zt Elevation of terrain above stack base

- Hc is calculated using the algorithm in CTDMPLUS using hc from AERMAP as:
Where:

NBrunt-Vaisala frequency

u(Hc)Wind speed at height Hc

hc Receptor specific terrain scale

- The fraction of the plume mass below Hc, as
- Weighting factor f is related to the fraction by

AERMOD’s Three Plume Treatment of the CBL

- Downdrafts more prevalent in CBL than the updrafts; the vertical concentration distribution is not Gaussian.
- Since larger percentage of the plume is affected by the downdrafts this ensemblage average has a general downward trend.
Instantaneous and corresponding ensemblage-averaged plume in the CBL

- The instantaneous plume is assumed to have a Gaussian concentration distribution about its randomly varying centerline
- The mean concentration is found by summing the concentrations due to random centerline displacements. This results in a skewed distribution which AERMOD presents as a bi-Gaussian p.d.f.
- AERMOD approach extends Gifford’s model to account for plume rise.
- The p.d.f. of the plume centerline height zc is
Where hs is the stack height, u is the mean wind speed and x is the downwind distance, ∆h is the plume rise including source momentum and buoyancy effects

- Direct or Real Source - describes the dispersion of the plume material that reaches ground directly from source via downdrafts
- Indirect Source - treats the plume sections that initially rise to the CBL top in updrafts and return to the ground via downdrafts
- Penetrated Source - accounts for the material that initially penetrates the elevated inversion height

- The total concentration in the CBL for the horizontal plume state is
Where:

Cc {xr, yr, zr}Total concentration in CBL

Cd {xr, yr, zr}Direct Source concentration contribution

Cr {xr, yr, zr}Indirect Source concentration contribution

Cp {xr, yr, zr}Penetrated Source concentration contribution

The total concentration for the terrain responding state has the form of the above equation by replacing zr with zp.

- Equation for concentration in SBL

- 5 different plume typed simulated based on the atmospheric stability and on the location and in and above the boundary layer
- Direct
- Indirect
- Penetrated
- Injected
- Stable

- During stable conditions, plumes are modeled with the familiar horizontal and vertical Gaussian formulations
- During convective conditions (L<0) the horizontal distribution is still Gaussian; the vertical concentration distribution results from a combination of the first three plume types.
- During convective conditions, AERMOD also handles a speaicl case referred to as an injected source where the stack top (or release height) is greater than the mixing height.

σy Standard deviation for lateral concentration

σz Standard deviation for vertical concentration

Case 1: Without a building

- Ambient turbulence
- Turbulence due to buoyancy
Case 2: Presence of a building

- Building wake effects

CONCENTRATION CALCULATIONS UNDER DOWNWASH

xDownwind distance from the upwind of the building to the receptoryCrosswind distance from the building centerline to the receptorzReceptor Height above groundσxgLongitudinal dimension of the wakeσygDistance from the building centerline to the lateral edge of the wakeσzgHeight of the wake at the receptor location

- Within the wake
- Use PRIME algorithm
- Beyond wake
- Use of PRIME and AERMOD
- CTotal = γ CPrime + (1- γ) CAERMOD
- When :

- Use of numerical plume rise model
- Use of AERMOD dispersion coefficients

- Air dispersion fundamentally based on the planetary boundary layer turbulence structure and scaling concepts
- The treatment of both surface and elevated sources in included
- Both simple and complex terrains are treated with the same set of equations