# Nonbuoyant Contaminant Sources

Gases, vapors, and small dust particulates are distributed in the space by air­flows produced by supply jets, convective flows, or air currents entering the building through the building apertures and cracks. Also, gases and vapors are distributed due to turbulent and molecular diffusion. Distribution of con­taminants with airflows is significantly faster (hundreds of times) than distri­bution due to molecular diffusion.

Theories of hood performance with nonbuoyant pollution sources are based on the equation of turbulent diffusion. The following equation allows the engineer to determine the contaminant concentration decay in the uniform airflow upstream from the contaminant source:

Where

X = distance from the source, m

C0 = contaminant concentration at the source, mg/m3

Cx = contaminant concentration at the distance X from the source, mg/m3

V = air velocity in the flow, m/s

D = coefficient of the turbulent diffusion, m2/s

The value of the coefficient of turbulent diffusion, D, depends upon the air change rate in the ventilated space and the method of air supply. Studies by Posokhin2 show that approximate D values for locations outside supply air jets is equal to 0.025 m2/s. Air disturbance caused by operator or robot movement results in an increase in the D value of at least two times. Studies by Zhivov et al.4 showed that the D value is affected by the velocity and direction of cross-drafts against the hood face, and the presence of an operator; e. g., for a cross-draft directed along the hood face with velocity v = 0.5 m/s with D = 0.15 m2/s (with the presence of an operator), an increase to v = 1.0 m/s results in D = 0.3 m2/s.

The quantity of contaminant (fume, oil mist, VOC, gas, or particulates), G, kg/h, generated in the space can be calculated using one of the following equations:

Where R1 is a fume, oil mist, VOC, gas, or particulate generation rate, kg/rnin, and T ess is an average contaminant release time per hour (e. g., arc rime for the welding process), min/h; or

 (7.4)

G = R2 x U,

Where R2 is a contaminant generation rate per production unit, kg/(produc — tion unit), and U is an average production unit output (e. g., units/h) for the given process.

For a welding process, for example, total welding fume generation rate R. is a fume (gas, particulate) generation rate, kg/min; Tarc is an average arc time for the welding process used, min/h; R2 is a fume generation rate, kg, per kg of electrodes used; and U is average electrode usage, kg/h, in the given welding process. Rj and R2, percentages of the critical components in the fume for the typical welding processes, and an average arc time for the typical welding pro­cesses are listed in AWS. J

Gas and Vapor Emission through Looseness

In Process Equipment and Pipelines

When the pressure inside the equipment/pipeline is greater than the room pressure, this emission can be calculated using the equation suggested by Repin:6

Where k is a reserve coefficient that varies from 1 to 2 depending upon the state of the equipment, C is a coefficient that depends upon the gas pressure inside the equipment (see Table 7.1), V is the internal volume of the equipment/pipeline with an excessive gas pressure (m3), m = molecu­lar weight of gas/vapor, and T = gas/vapor temperature inside the equip­ment (°C).

Gas and Vapor Emission Processes from an Open Liquid Face

Emission from an open liquid face (e. g., open tanks, liquid spills on the floor surface) can be evaluated using equations based on criteria relations and empirical data. Assuming that the heat and mass transfer processes can be de­scribed using similar differential equations, the criteria equation describing the evaporation process will be similar to one describing the heat transfer:3

Nu = C(Gr ■ PR)”,

Where Nu, Gr, and Pr are the Nusselt, Grashof, and Prandtl numbers for evap­oration processes:

Rr = g^3(Pp-Pi)

V_7I —

 TABLE 7.1 Coefficient C

 Gas Pressure, Atmospheres < 2

 17

 100 !

 41

 401

 161

0.

 C

121 0.166 0.182 0.189 0.152 0.289 0.297 0.370

Where

G0 = mass rate of liquid evaporation (liquid mass evaporated from unit of surface area in a unit of time, and related to the unit of vapor concentration at the surface and in the ambient air), m/s d = characteristic dimension, m D = molecular diffusion coefficient, m2/s v = kinematic viscosity coefficient, m2/s p0 = ambient air density, kg/m3

P! = air density near the liquid surface at the surface temperature, kg/m3

Film Regime In the film regime, there is a thick film of undisturbed air formed adjacent to the liquid surface (e. g., evaporation from the surface of small mercury droplets). In Eq. (7.6), Grx Pr < 1, n = 0, and Nu is con­stant.

The mass flow rate, G, g/s, from the surface can be evaluated using

G = 2Dd(C1 — C0),

Where C, and C0 are vapor concentration, g/m3, in the air adjacent to the liq­uid surface and in the ambient air.

Laminar Regime In the laminar regime, 2 x 102 < Gr x Pr < 2.3 x 108, and n = 1/4. The mass flow rate, G, g/s, from the surface can be eval­uated using

 (7.8)

G = FAd-x/4D1/2(C1 — C0)5/4|(Mair/M; — 1)|1/4

Where Mair = relative molecular weight of air, Mt = relative molecular weight of vapor evaporated from the liquid surface, and A = surface area, nv2.

For a horizontal surface, F = 0.334 when Mak > M(, and F = 0.184 when Mair < Mj. For a wet vertical surface, F = 0.224.

Turbulent Regime In the turbulent regime, Gr x Pr > 2.3 x IQ8, and n = 1/3. This regime may occur only when the area of evaporating liquid is very large (tens of square meters).

The mass flow rate, G, g/s, from the surface can be evaluated using

 (7.9)