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# HW3 6130 Solution

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Homework III (due 03/04/2010)

1. A filter bed of packing density 0.1 and fiber diameter 4 m for use in removing radioactiveparticles from a gas stream must provide an overall collection efficiency of at least 99.99%

for particles of any size. Given a flow rate of air at 298 K, 1 atm of 1 m3/s, p = 1.2 g/cm3,

and filter bed width and height of 1.5 and 1.0 m, respectively, determine (a) the necessarydepth of the filter; (b) the most penetrating particle size (MPPS) and the corresponding

single fiber efficiency; (c) the relative importance of single fiber efficiency due tointerception, impaction and diffusion in collecting the MPPS; (d) filter quality at the

MPPS. (16%)

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2. With increasingly stringent fuel economy standards, diesel engines appear to be attractive

alternative power plants for passenger vehicles. However, despite its superior fueleconomy, a diesel engine presents a challenging emission control problem. As the engine

is operated in a manner to maintain low NOx emissions, particulate emissions exceed theexhaust standard. Thus, an additional scheme for controlling particulate emissions isnecessary. One such scheme that has received extensive study is the filtration of exhaust

particulate matter by a filter bed placed in the exhaust system. In this problem, weconsider the design of a fibrous filter bed for this purpose. (Disposal of the collected

particulate matter is a key problem, although we do not consider it here.) We will focus on

the initial performance of the filter, that is, on the period during which the deposition of

particles is not influenced by those already collected. The following conditions can be

assumed for the exhaust filtration problem: = 0.05, T = 473 K, df= 10 m, u = 8 cm/s,

and p = 1 g/cm3.

(a)Calculate the Stokes number for particles ranging in size from 0.02 to 1.0 m indiameter. Show that the Stokes number is sufficiently small that inertial impaction can

be neglected as a significant mechanism of collection.

Stokes numbers from 0.02 to 1.0 m are sufficiently small to neglect the impaction.

(b)Plot the single fiber collection efficiency as a function of particle diameter over therange 0.02 to 1.0 m showing the individual contributions of diffusion and interception

Assume the Kuwabawa flow field to be applicable.

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Diffusion is dominant mechanism for small size particles whereas interception is moreimportant for large size particles.

(c)For a given set of operating conditions there are four filter design parameters that canbe varied: filter face area, filter thickness, fiber size and packing density. These design

parameters can be divided into two groups; the first two parameters are related to the

0.01 0.1 1

0.00

0.05

0.10

0.15

0.20

0.25

Efficiency

Dp

Diffusion

Interception

Efficiency for single fiber

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size and shape of the filter, and the last two refer to the properties of the filter medium.Considering the operating conditions corresponding to an Oldsmobile 5.7-L diesel

engine automobile being drive at 40 mph (64 km/h):Exhaust flow rate = 2832 L/min (at 293 K, 1 atm)

Exhaust temperature = 473 K

Mass median particle diameter = 0.2 m

Particle density = 1 g/cm3

With filter thickness as the ordinate (in cm) and filter face area as the abscissa (in cm2),plot the curve of overall bed efficiency = 90% based on particle mass. (If we require at

least 90% efficiency, all points above this line are candidates for a filter design).

(d)Now assuming a filter face area of 2500 cm2 and a thickness of 3.4 cm, with theoperating conditions above, plot the overall bed efficiency as a function of packing

density over the range 0 < < 0.1 fordf= 5, 10, 20 and 40 m. Discuss your results.

(24%)

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The overall efficiency increases as the solidity increases because of increase of crosssectional area. The overall efficiency decreases as the fiber diameter increases in that

the diffusion and interception decrease.

3. (a) An aerosol neutralizer has a volume of 1.7 L and contains a 1.0-mCi Kr-85 source thatproduces an ion concentration of 3106 #/cm3 inside the cylinder. At a flow of 50 L/min,what fraction of the original charge will remain on an aerosol after it has passed through

the device? (b) What is the average charge on a 0.15 m diameter particle in equilibrium

with bipolar ions at 293 K? (12%)

0.00 0.02 0.04 0.06 0.08 0.10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Efficiency

Packing density ()

df=5

df=10

df=20

df=40

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4. For the particle size range listed below and E = 2 kV/cm, determine the collectionefficiency of a plate-type electrical precipitator. The plate spacing is 1 inch and the platelength in the direction of flow is 5 ft. Make your calculations for velocities of 3 and 10

ft/s, and plot efficiency as a function of particle diameter. Assume flat collecting plates

and a laminar flow. Also, Nit = 108 s/cm3, = 10 and T = 300K. (20%)

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dp (m) Wt% (< dp)

< 0.1 5

0.3 10

0.6 50

1 90

5 99.6

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5. Raindrops falling from thunderclouds may carry charges as high as 3.310-11 C/drop.What is the minimum size of such drops? (6%)

6. The California visibility standard requires that the visibility be greater than 10 miles ondays when the relative humidity is less than 70%. Consider a day when the visibility

0.1 10

10

20

30

40

50

60

70

80

90

100

110

Collectionefficiency(E

)

Particle diameter (m)

3 ft/s

10 ft/s

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controlling aerosol is composed of material with a refractive index of 1.5. Estimate the

aerosol mass concentration (g/m3) in the atmosphere that would correspond to the

visibility standard. Assume (1) the density of the spherical particles is 1 g/cm3; (2) the

aerosol is monodisperse with a particle size, dp = 0.5 m; and (3) the wavelength of

interest is 0.5 m. (8%)

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7. (a) What is the maximum distance at which one can see a black automobile on a foggy,moonlit night? Assume that the fog consists of 5 m droplets at 1010 #/m3, that the

background luminance is 10-3 cd/m2, and that your eyes are completely dark adapted. (b)Repeat part (a) if the headlights are on and are directed toward you; assume the inherent

contrast is 104. (10%)

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8. Let Jbe the intensity of the air light seen by an observer looking along a horizontal path tothe horizon sky (infinity). The path falls close to one that ends at a black test object a

distancex from the observer. Show that the intensity of the light seen by an observerlooking toward the black test object is given by

)1()( xeJxI

(b) Derive an expression for the fraction of the total air light (to infinity) contributed by the

atmosphere between the observer and the point x from the observer. (12%)

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9. Go over the Optical Particle Counter module athttp://aerosol.ees.ufl.edu. Learn how tooperate the OPC simulator. Use it to simulate the measurement of room air and outdoor

air in St. Louis. Present your results and discuss how the size distributions are different.(10%)

For both room air and outdoor air, the number concentration decrease as particle sizeincreases. The number concentration in outside is higher than that in room air. The

possible reason is anthropogenic sources such as construction and combustion. The filteredair through HVAC system goes into the building (room).

0.2 0.4 0.6 0.8 1.0 1.2 1.4-2.0x10

4

0.0

2.0x104

4.0x104

6.0x104

8.0x104

1.0x105

1.2x105

1.4x105

1.6x105

1.8x105

NumberC

oncentation(#/cm

3)

Particle Diameter (m)

Room Air

Outside

http://aerosol.ees.ufl.edu/http://aerosol.ees.ufl.edu/http://aerosol.ees.ufl.edu/

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