Plane Plume

One of the effects of wind speed is to dilute continuously released pollutants at the point of emission. Whether a source is at the surface or elevated, this dilution takes place in the direction of plume transport. Figure 19-2 shows this effect of wind speed for an elevated source with an emission of 6 mass units per second. For a wind speed of 6 m s", there is 1 unit between the vertical parallel planes 1 m apart. When the wind is slowed to 2 m s there are 3 units between those same vertical parallel planes 1 m apart. Note that this dilution by the wind takes place at the point of emission. Because of this, wind speeds used in estimating plume dispersion are generally estimated at stack top. 

Note that if y = 0, or 2 = 0, or both 2 and H are 0, this equation is greatly simplified. For locations in the vertical plane containing the plume center-line, y = 0 and gi = 1. 

The vertical motion of the plume to the height where it becomes horizontal is known as the plume rise, (refer back to Figure 1). The plume rise is assumed to be a function primarily of the emission conditions of release, (i.e. velocity and temperature characteristics). A velocity in the vertical plane gives the gases an upward momentum causing the plume to rise until atmospheric turbulence disrupts the integrity of the plume. At this point the plume ceases to rise. This... 

In reality, heat sources are seldom a point, a line, or a plane vertical surface. The most common approach to account for the real source dimensions is ro use a virtual source from which the airflow rates are calcu-lared " " see Fig. 7.64. The virtual origin is located along the plume axis at a distance on the other side of the real source surface. The adjustment of the point source model to the realistic sources using the virtual stmrce method gives a reasonable estimate of the airflow rate in thermal plumes. The weakness of this method is in estimating the location ol the virtual point source. 

Radiation heat flux is graphically represented as a function of time in Figure 8.3. The total amount of radiation heat from a surface can be found by integration of the radiation heat flux over the time of flame propagation, that is, the area under the curve. This result is probably an overstatement of realistic values, because the flame will probably not bum as a closed front. Instead, it will consist of several plumes which might reach heights in excess of those assumed in the model but will nevertheless probably produce less flame radiation. Moreover, the flame will not bum as a plane surface but more in the shape of a horseshoe. Finally, wind will have a considerable influence on flame shape and cloud position. None of these eflects has been taken into account. 

The assumptions made in tlie development of Eq. 12.6.1 are (1) tlie plume spretid lias a Gaussian distribution in both tlie horizontal and vertical planes witli standard deviations of plume concentration distribution in the horizontal and vertical of Oy and respectively (2) tlie emission rate of pollutants Q is uniform (3) total reflection of tlie plume takes place at tlie eartli s surface and (4) tlie plume moves downwind with mean wind speed u. Altliough any consistent set of units may be used, tlie cgs system is preferred. 

Elevated Plumes can be trapped either above or below the base of the inversion and held in a horizontal plane. Again, these can be brought down to ground level by eddies. This process is known as fumigation and can result in short-term high-level concentrations. 

Jensen Webb (Ref 43) examined the data predicting the extent of afterburning in fuel-rich exhausts of metal-modified double-base proplnt rocket motors so as to determine the amt of an individual metal which is required to suppress this afterburning. The investigatory means they used consisted of a series of computer codes. First, an equilibrium chemistry code to calculate conditions at the nozzle throat then a nonequilibrium code to derive nozzle plane exit compn, temp and velocity and, finally, a plume prediction code which incorporates fully coupled turbulent kinetic energy boundary-layer and nonequilibrium chemical reaction mechanisms. Used for all the code calcns were the theoretical environment of a static 300 N (67-lb) thrust std research motor operating at a chamber press of S.SMNm 2 (500psi), with expansion thru a conical nozzle to atm press and a mass flow rate... 

Figure 11. Dosage intensities 10 12 (min liter ) in a horizontal plane (at 1 m) and in vertical planes along the plume center lines of fluorescent particles released in a 27 m Douglas fir forest. Isolines are in powers of 10. Release points, and plume center lines are shown and - - respectively. (a) release at 1 m (b) release at 10 m and (c) release at 20 m. Average temperature profiles and wind direction (- ) and speeds are shown for selected towers and heights. (From 20).

FIGURE 3.9 Migration of the contaminant plume for the point source. The sliding planes in the X, Y, and Z directions show the position of the soil column regions in which the solute concentration complies with EPA criteria for Hg in fresh water. The numerical value of the maximum concentration in those planes is also shown. 

FIGURE 3.10 Migration of the contaminant plume for the line source. Only two visualization planes are shown (horizontal and transverse) because of the almost symmetric contaminant distribution in the longitudinal plane. 

FIGURE 3.11 Migration of the contaminant plume for the two-point source. The advective and dispersive contaminant front is visualized at planes in which the solute concentration complies with the EPA criteria. Concentrations at the frontmost and backmost planes, however, are shown to be over the CMC and CCC limits. 

Note tliat this is the coordinate system used by most engineers.) The origin is at ground level at or beneath the point of emission, with the x a.xis extending liorizonially in the direction of the mean wind. Tlie y axis is in tlie horizontal plane perpendicular to tlie x axis, and tlie z axis extends vertically. The plume travels along or parallel to the x axis (in tlie mean wind direction). 

Fig. 5 shows the bubble plume in front view (y-z plane) and profile (z-x plane). In both cases the photo is accompanied by a drawing schematizing the observed flows. For a constant gas input, the total gas/liquid contact surface is greater for small bubbles than for larger bubbles and the gas-liquid interactions are also greater. It was observed that the smaller the bubbles, the greater the liquid velocity, the more agitated and more turbulent the bubble plume, and the more spread out the plume at the air/liquid interface. 

Figure 2.16 Distorted plume caused by canyon winds and diffusion from an elevated source. Plume boundaries (defined a fixed ratio, e.g. 1/10 of centerline concentration at given value of x) in horizontal plane, showing components unentrained (dash-dot line), detrained (dashed line) and plume in canyon below building height (shading).

The effect of temperature stratification on the atmosphere can be illustrated by considering the different forms a plume may assume. The form of a plume is determined essentially by the relation of the plume release point to any stable, neutral, and unstable layers that may be present the basic forms have been summarized by Slade (1968) and Arya (1999). In a stable layer, vertical mixing of the plume will be limited, and the plume will fan out in the horizontal plane. If a plume is released into a neutral layer capped by a stable layer, the plume will mix vertically throughout the entire depth of the neutral layer. If a plume is released into a neutral layer... 

---