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Algorithms II · atmospheric pollution Applications 1: air pollution modeling software · flare stacks · odor units · air dispersion models · environmental GIS · environmental reports · indoor air quality · environmental health · environmental risk assessment · stack testing · atmospheric pollution · air modeling · gas dispersion
Plume Rise Formulas The plume height is used in the calculation of the Vertical Term. The distance dependent momentum plume rise equations are used to determine if the plume is affected by the wake region for building downwash calculations. Stacktip Downwash. In order to consider stacktip downwash, modification of the physical stack height is performed. The modified physical stack height h_{s} is found from: h_{s}’=h_{s}+2d_{s}[(v_{s}/u_{s})1.5] for v_{s}<1.5u_{s} (5) or h_{s}’=h_{s} for v_{s}> o =1.5u_{s} (6) where h_{s} is physical stack height (m), v_{s} is stack gas exit velocity (m/s), and d_{s} is stack top diameter (m). If stack tip downwash is not considered, h_{s}’= h_{s} in the following equations. Buoyancy and Momentum Fluxes. For most plume rise situations, the value of the Briggs buoyancy flux parameter, F_{b} (m^{4}/s^{3}), is needed F_{b}=gv_{s}d_{s}^{2}(DT/4T_{s}) (7) where DT = T_{s}  T_{a}, T_{s} is stack gas temperature (K), and T_{a} is ambient air temperature (K). For determining plume rise, the momentum flux parameter, F_{m} (m^{4}/s^{2}), is calculated based on the following formula: F_{m}=gv_{s}^{2}d_{s}^{2}(T_{a}/4T_{s}) (8) Unstable or Neutral  Crossover Between Momentum and Buoyancy. For cases with stack gas temperature greater than or equal to ambient temperature, it must be determined whether the plume rise is dominated by momentum or buoyancy. The crossover temperature difference, (DT)_{c}, is determined as follows: for F_{b} < 55, (DT)_{c}=0.0297 T_{s}(v_{s}/d_{s}^{2})^{1/3} (9) and for F_{b} >= 55, (DT)_{c}=0.00575 T_{s}(v_{s}^{2}/d_{s})^{1/3} (10) If DT, exceeds or equals (DT)_{c}, plume rise is assumed to be buoyancy dominated, otherwise plume rise is assumed to be momentum dominated. Unstable or Neutral  Buoyancy Rise. For situations where DT exceeds (DT)_{c} as determined above, buoyancy is assumed to dominate. The distance to final rise, x_{f}, is assumed to be 3.5x^{*}, where x^{*} is the distance at which atmospheric turbulence begins to dominate entrainment. The value of x_{f} is calculated as follows: for F_{b} < 55: x_{f}=49F_{b}^{5/8} (11) and for F_{b} >= 55: x_{f}=119F_{b}^{2/5} (12) The final effective plume height, h_{e} (m), is determined as for F_{b} < 55: h_{e}=h_{s}+(21.425 F_{b}^{3/4}/u_{s}) (13) and for F_{b} = 55: h_{e}=h_{s}+(38.71 F_{b}^{3/5}/u_{s}) (14) Unstable or Neutral  Momentum Rise. For situations where the stack gas temperature is less than or equal to the ambient air temperature, the assumption is made that the plume rise is dominated by momentum. If DT is less than (DT)_{c}, the assumption is also made that the plume rise is dominated by momentum. The plume height is calculated as: h_{e}=h_{s}+3d_{s}(v_{s}/u_{s}) (15) Briggs suggests that this equation is most applicable when v_{s}/u_{s} is greater than 4. Stability Parameter. For stable situations, the stability parameter, s, is calculated: s=g[(dT/dz)/T_{a}] (16) As a default approximation, for stability class E (or 5) dT/dz is taken as 0.020 K/m, and for class F (or 6), dT/dz is taken as 0.035 K/m. Stable  Crossover Between Momentum and Buoyancy. For cases with stack gas temperature greater than or equal to ambient temperature, it must be determined whether the plume rise is dominated by momentum or buoyancy. The (DT)_{c} is determined and solving for DT, as follows: (DT)_{c}=0.019582 T_{s} v_{s} s^{1/2} (17) If the difference between DT exceeds or equals (DT)_{c}, plume rise is assumed to be buoyancy dominated, otherwise plume rise is assumed to be momentum dominated. Stable  Buoyancy Rise. For situations where DT exceeds (DT)_{c} as determined above, buoyancy is assumed to dominate. The distance x_{f} is determined by x_{f}=2.0715 u_{s} s^{1/2} (18) The plume height, h_{e}, is determined by h_{e}=h_{s}+2.6 [F_{b}/(u_{s}s)]^{1/3} (19) Stable  Momentum Rise. Where the stack gas temperature is less than or equal to the ambient air temperature, the assumption is made that the plume rise is dominated by momentum. Then, h_{e}=h_{s}+1.5[F_{m}/(u_{s}s^{1/2})]^{1/3} (20) The equation for unstableneutral momentum rise is also evaluated. The lower result of these two equations is used as the resulting plume height. atmospheric pollution
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