TRANSPORT OF A BACTERIAL AEROSOL IN
TURBULENT MIXING REGIONS

Thesis for ”W Degree of ph. D.
MIEEISM STATE UNIVERSITY
Dennis Ray I-EeIdman

1965

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ABSTRACT

TRANSPORT OF A BACTERIAL AEROSOL IN
TURBULENT MIXING REGIONS

by Dennis Ray Heldman

The knowledge of transport mechanisms of bacterial
aerosols is, of primary importance when analyzing air-
borne contamination control methods for food processing
and packaging operations. This investigation was con-
ducted to determine the transport characteristics of a
bacterial aerosol under conditions simulating two adjacent
rooms with different aerosol concentrations. The experi-
mental investigation involved determination and description
of transfer coefficients for transport of an aerosol
through an opening in a partition between two 64 ft3
compartments with different uniform aerosol concentrations.
Theoretical description and analysis of experimental data
involved the use of a mixing region model, which described
turbulent dispersion of aerosol through the opening and
entrainment in the low concentration compartment.

Air velocity fluctuations were detected by a hot wire
anemometer and recorded for several locations and flow
conditions. Information on turbulent energy, eddy diffusivi-

ties and dispersion of the aerosol in the mixing region was

Dennis Ray Heldman

obtained by means of a statistical analysis of the
-air velocity records.

Experimental data were collected for equal air
flow rates from 20 to 60 ft3/min through both compartments
of the aerosol chamber. In addition, tests were conducted
with air/flow rate gradients as high as 40 ft3/min in the
same direction or opposite the concentration gradient.
Transfer coefficients and turbulent energy increased sig-
nificantly as air flow rate increased from 20 to A0 ft3/min,
whereas the intensity of turbulence was relatively constant
over the entire range investigated. For aerosol flow
rates above 30 ft3/min, transfer coefficients were maximum
when air flow rates through both compartments were equal.

The area of the opening between the two compartments
was varied by changing the vertical height to 3, 6, and 9 in.
Decreasing transfer coefficients with increasing vertical
height of opening were related to the shape of the mixing
region profiles.

The partition width at the initial point of mixing
influenced the transfer coefficients slightly. An increase
in transfer coefficient occurred as the width was increased
from 0.0625 to 0.3125 in., but the coefficient decreased as
the width was increased to 0.5625 in. Slight increases in
turbulence due to increased partition width and a reduction
in mixing region width were factors involved in the

explanation of this relationship.

Dennis Ray Heldman

The influence of temperature gradients on transport
characteristics was determined by heating the air in one
compartment of the aerosol chamber. Transfer coefficients
increased consistently as the temperature gradient was
increased from -lA° to +12.5°F

A dimensionless relationship was derived, based on
the turbulent mixing region model, and used to present all

data obtained in the investigation.

Approved png M

Major Professor
and Department Chairman

2L.“ 39,/465

Date

TRANSPORT OF A BACTERIAL AEROSOL IN

TURBULENT MIXING REGIONS
By

Dennis Ray Heldman

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1965

ACKNOWLEDGMENTS

The guidance and leadership of Dr. C. w. Hall,
chairman of the Agricultural Engineering Department, is
gratefully acknowledged. The inspiration provided through-
out this portion of my graduate program and during the
course of this investigation has made it a pleasing and
rewarding experience.

Sincere appreciation is extended to Dr. T. I.
Hedrick (Food Science) for supplying facilities required
for conducting experiments and for providing advice and
suggestions whenever requested.

Additional acknowledgment is offered to Dr. K. L.
Schulze (Sanitary Engineering) and Dr. F. H. Buelow
(Agricultural Engineering) for serving as guidance
committee members and providing advice whenever needed.

The unfailing support and encouragement provided by
my wife, Joyce, has supplied inspiration needed throughout

my undergraduate and graduate education.

ii

To:

Joyce, Cynthia and Candace
Mr. and Mrs. M. L. Heldman
Mr. and Mrs. H. S. Anspach

iii

TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS . . . . . . . . . . . . . ii
LIST OF TABLES. . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . viii
LIST OF APPENDICES . . . . . . . . . . . . xi
NOMENCLATURE . . . . . . . . . . . . . . xii
Chapter

1. INTRODUCTION 1
2. LITERATURE REVIEW u
2.1. Characteristics of Air-Borne Bacteria. A
2.1a. Existence. . u
2.1b. Sedimentation and Deposit 5
2.10. Viability. . . . 7
2.1d. Sampling 9

2.2. Production and Study of Uniform Bacterial
Aerosols . . . . . . . . . 11
2.2a. Production of the Aerosol . . . 11
2.2b. The Aerosol Chamber . . . . . 13
2.3. Transport Processes. . . . . . . . IA
2.3a. Turbulence . . . . . . 14
2.3b. Turbulent Diffusion . . . . 16
2.3c. Transport in Mixing Regions. . . 25
3. THEORETICAL CONSIDERATIONS . . . . . . . 29
3.1. Basic Diffusion Equations. . . . . . 32
3. 2. Turbulent Diffusion. . . . . . 37
3. 3. Turbulent Transfer Coefficient . . . . 39
3.4 Eddy Diffusivity . . . . . 41
3.5 Transport in the Mixing Region . . . . ug

iv

3.5a. Isovel- Isothermal Flow. .
3.5b. Turbulent Mixing with Unequal
Velocities
3.50. Influence of Partition Width.
3.5d. Turbulent Mixing with a Temperature
Gradient.
4. EXPERIMENTAL PROCEDURES AND EQUIPMENT
4.1. Equipment
4.1a. Aerosol Chamber
4.1b. Aerosol Generation
4.1c. Air Sampling . .
4.1d. Air Velocity and Turbulence
4.2. Bacteriological Methods.

4.2a. Handling Techniques.
4.2b. Plating and Counting

4.3. Scope of Tests.
4.3a. Turbulent Transfer Coefficient
4.3b. Eddy Diffusivities . .
4.3c. General Procedures
4.4. Analysis of Turbulence Data
5. RESULTS AND DISCUSSION

5.1. Characteristics of the Aerosol Chamber.
5 Turbulent Diffusion . . . .

5.2a. Turbulent Energy. .
5.2b. Autocorrelation Coefficients.

5.3. Concentration Distributions
5.4. Transport of the Bacterial Aerosol

5.4a. Experimental Transfer Coefficients.

5.4b. Dimensionless Relationships
6. CONCLUSIONS.
7. RECOMMENDATIONS FOR FUTURE WORK
APPENDIX
REFERENCES

Page
43

46
46
48
48
48

E
J

58
58

60
60

61
61
63
63
64
67

67
73

73

85
86

86
92

102
105

106

. 126

LIST OF TABLES

Influence of relative humidity on death rate
constants of Serratia marcescens. .

 

Summary of results

Pressure drop, air flow rate and mean air
velocity.

Influence of air flow rate on transport
charactgristics of air-borne bacteria with
1.5 ft opening

Influence of air flow rate gradient on trans-
port characteristics of air-borne bacteria
with 1.5 t 2 opening and aerosol flow rate
of 30 ft /min. . .

Influence of air flow rate gradient on trans-
port charactsristics of air-borne bacterial
with 1.5 t opening and aerosol flow rate
of 40 ft /min. .

Influence of air flow rate gradient on trans-
port charactSristics of air-borne bacteria
with 1.5 t opening and aerosol flow rate
of 50 ft /min. . .

Influence of width at initial point of mixing
on transport characteristics of air-borne
bacteria" at 50 ft 3/min

Influence of width at the initial point of
mixing on transport characteristics of air—
borne bacteria at 40 ft /min. .

Influence of width at initial point of mixing
on transport characteristics of air-borne
bacteria at 30 ft 3/min

Influence of air flow rate gradient on trans-
port characteristics of air-borne bacteria
with 0.3125 in. partition

vi

Page

80

108

112

113

114

115

116

. 117

. 118

. 119

Table

Page
A.10. Influence of air flow rate gradient on trans—
port characteristics of air—borne bacteria
with 0.5625 in. partition. . . . . . . 120
A.11. Influence of air flow rate gradient on trans-
port charac eristics of air-borne bacteria
with 1.0 ft opening . . . . . . . . 121
A.12. Influence of air flow rate gradient on trans-
port charac eristics of air—borne bacteria
with 0.5 ft opening . . . . . . . . 122
A.13. Influence of temperature gradient on trans—
port characteristics of air-borne bacteria
at 61 ft3/min. . . . . . . . . . . 123
A.14. Turbulence data at various locations and flow
conditions . . . . . . . . . . . 12“
A.15. Dispersion data at various locations and flow
conditions . . . . . . . . . . . 125

vii

Figure

4.1.

4.3.

4.4.

4.5.
4.6.

4.9.

4.10.

4.11.

4.12.

5.1.

5.3.

5.4.

LIST OF FIGURES

viii

Page

Temperature and relative humidity recording

instruments . . . . . . . . . 49
Schematic diagram of aerosol chamber and

related instrumentation 50
Partition and opening between compartments

of aerosol chamber 51
Air diffuser in ceiling of one compartment of

aerosol chamber 51
Ultra—high efficiency air filter 53
Venturi tube and micromanometer used for air

flow measurement 53
Casella slit air sampler. 55
Prechamber and related parts of aerosol gen-

eration system 55
Aerosol atomizer and culture reservoir 57
Air sampling station and point of aerosol

injection into duct 57
Hot wire anemometer and auxilary equipment. 59
X-Y recorder. 59
Dynamic emptying characteristics of aerosol

chamber 68
Variation of turbulent energy and intensity of

turbulence with air flow rate . . . 71
Influence of transverse location on intensity

of turbulence. 71
Variation of turbulent energy in transverse

direction . . 74

Figure Page

 

5.5. Agreement of experimental data with equation

3.16. . . . . . . . . . . . . . 74
5.6. Turbulent energy profiles with 70 ft3/min on

high air flow rate side . . . . . . 76
5.7. Turbulent energy profiles with 60 ft3/min on

high air flow rate side . . . . . . . 76
5.8. Turbulent energy profiles with 50 ft3/min on

high air flow rate side . . . . . . 76
5.9. Autocorrelation coefficients as influenced by

time lag . . . . . . . . . . . . 79
5.10. Variations in apparent mixing region width with

air flow rate and partition height. . . . 79
5.11. Concentration distribution in mixing region . 87
5.12. Variation of transfer coefficient with air

flow rate . . . . . . . . . . . . 89
5.13. Influence of air flow rate gradient on trans-

fer coefficient . . . . . . . . . . 89
5.14. Influence of temperature gradient on trans-

fer coefficient . . . . . . . . . . 91
5.15. Influence of temperature and relative humidity

on death rate of Serratia marcescens . . . 91
5.16. Influence of aerosol viability on the relation-

ship between temperature gradient and trans-

fer coefficient . . . . . . . . . . 91
5.17. Dimensionless transport as influenced by

turbulence, dispersion time and mean air

velocity . . . . . . . . . . . . 93
5.18. Variation in dimensionless transport with air

flow rate gradient for aerosol flow rate of

50 ft3/min. . . . . . . . . . . . 96
5.19. Variation in dimensionless transport with air

flow rate gradient for aerosol flow rate of

40 ft3/min. . . . . . . . . . . . 96

ix

Figure Page

5.20. Variation in dimensionless transport with air
flow ate gradient for aerosol flow rate of

30 ft /min. . . . . . . . . . . . 96
5.21. Influence of partition width on dimensionless

transport . . . . . . . . . . . . 98
5.22. Influence of opening height on dimensionless

transport . . . . . . . . . . . . 98
5.23. Influence of the dimensionless temperature

ratio on dimensionless transport . . . . 98

5.24. Experimental correlation of dimensionless
groups involved in bacterial aerosol trans—

port. . . . . . . . . . . . . . 101

A.l. Mean air velocity profile . . . . . . . 110

Appendix

A.1.

LIST OF APPENDICES

Air Flow Measurement
Solution to Diffusion Equation
Mean Air Velocity Profile.

Experimental Turbulent Transfer
Coefficients

xi

Page
107
108

111

111

NOMENCLATURE
apparent width of aerosol mixing region defined
by equation (3.36), in.
partition width at initial point of mixing, in.
bacterial aerosol concentration, No./ft.3

bacterial aergsol concentration at time equal to
zero, No./ft.

apparent Eddy diffusivity presented in equation
(3.3), in /min.

specific egdy diffusivity defined by equation
(3.32), in /min.

air flow rate, ft3/min.

air flow rate with equal flow in both compart—
ments of aerosol chamber, ft /min..

integral of complementary error function defined
in equation (3.47), in.

vertical height of Opening between compartments
of aerosol chamber, in.

vertical height of aerosol chamber.

length scale of turbulence defined in equation

(3.34), in-
death rate constant of bacterial aerosol, l/min.
experimental constant in equation (3.42).

turbulegt transfer coefficient, No./ft2,min
(No./ft ).

mass flux of bacterial aerosol, No./min.

autocorrelation coefficient defined in equation

(3.21)

xii

‘14

0‘t

aerosol dispersion time, min.
time required for R(§) to approach zero, sec
air velocity parallel to x—axis, ft/min.

turbulent energy factor for longitudinal direction,
ft2/min2

air velocity parallel to y—axis, ft/min.

turbulent energy factor for transverse direction,
ftZ/min2

volume of one compartment in aerosol chamber, ft3

rectangular coordinate parallel to vertical
direction in aerosol chamber

rectangular coordinate transverse to opening
between compartments of aerosol chamber

statistical dispersion length defined by equation
(3.25). 1m?

turbulent thermal diffusivity, in2/min.

coefficient defined in equation (3.40).

-temperature, °F.

absolute temperature, °R.
kinematic viscosity, in2/min
turbulent viscosity, ine/min

time lag in instantaneous velocity correlations,
sec

Bar above symbol indicates mean component
Prime above symbol indicates instantaneous component

Subscripts:

H refers to compartment with highest magnitude

L refers to compartment with low magnitude

xiii

1. INTRODUCTION

A small percentage of the 1,500,000 particles in an
average cubic foot of air are viable microorganisms. How-
ever, the existence of these viable bacteria in the air of
dairy and food processing plants is of greater importance
than the small percentage indicates. Reports on the
populations of air—borne microorganisms are varied both in
approach and results. Olson and Hammer (1934) and Cerna
(1961) reported counts as high as 12 and 55, respectively,
settling on a standard size petri dish per minute in
various areas of dairy plants. Labots (1961) and Heldman
§t_a1. (1964) reported mean counts of 5 to 85 per ft3 when
using vacuum slit samplers. The fact that populations of
air-borne microorganisms exist in food processing areas
can be attributed to the many sources present in these
areas. Isolation of floor drains as a source of air—
borne microorganisms during flooding is just one example
(Heldman 92:11., 1965).

The existence of an air-borne microorganism popula—
tion of any magnitude provides a chance for air-borne
contamination of exposed products. In many cases, this
contamination may occur after processing and will result

in significant reductions in product shelf-life. The

importance of this type of contamination is increasing
significantly due to the prOSpects of packaging sterile
products such as milk and other milk products. Contamin—
ation of the sterile product with a single microorganism
will result in an unacceptable storage life for these
products.

The deveIOpment of ultra—high efficiency or
ABSOLUTE filters for air may solve at least part of the
air-borne contamination problem. These filters, which are
designed to remove 99.97% of all 0.3 micron particles,
will provide air which is practically free of air-borne
microorganisms. However, the more difficult and unsolved
problem is that of secondary contamination or contamination
of the filtered air from the many sources of air-borne
microorganisms in the processing plant. A partial solution
to the latter problem is localized control by use of "laminar
air flow" (Whitfield, 1963) or jets of filtered air to
protect selected spaces. These mthods are limited, however,
to small spaces and much is unknown about the effectiveness
of laminar air flow in the mixing regions.

Before complete control of air—borne contamination
can be attained, basic information on the transport of
air-borne microorganisms from the source to the product
must be obtained. Within a room, the movement and flow
patterns of the air is of major concern. However, when
considering transport of air-borne microorganisms from

one room to an adjoining room, factors such as the mixing

of two air streams at openings between rooms is of importance.
Unless there is considerable momentum transport or air
movement through the Openings, the mixing of the air streams
must provide the major portion of the transport. In addition,
the mixing of a high concentration air stream with a low
concentration air stream may be influenced by other vari—
ables such as flow conditions of the air streams, geometry
at the initial point of mixing and differences in tempera—
ture and relative humidity between the air streams.

The purpose of this investigation is to determine
the transport characteristics of air—borne microorganisms
in a mixing region which would simulate that encountered
between two rooms with different air-borne concentrations.
The results obtained should not be limited to food and
dairy processing plants because of the wide-spread interest
in the same subject in hospitals and "dust free" rooms.
Mixing regions are also encountered in many contamination
control devices, and results obtained in this investigation

may lead to improved control methods.

2. LITERATURE REVIEW

2.1 Characteristics of Air-Borne Bacteria

The develOpment of procedures and techniques for the
study of air—borne bacteria has occurred, to the greatest
extent, in the last 15 to 20 years. The stimulation of
these developments has been related mostly to: (a)
increased frequency of air—borne infection by antibiotic
resistant strains of bacteria in hospitals and (b) the

possibilities of biological warfare.

2.1a Existence

 

Air—borne bacteria exist as aerosols, which are
defined as liquid or solid particles in air. According
to Wolf, g§_gl. (1959), the biological particles may
exist in any of the following forms: (a) single unattached
cells, (b) clumps composed of a number of microorganisms,
(c) cells adhering to a dust particle, or (d) a free
floating microorganism surrounded by a film of dried organic
or inorganic material. In addition, the microorganism
involved may be a vegetative cell or a spore. The relative
importance of vegetative cells as compared to spores depends
on the air space involved. Wolf, et_al, (1959) indicates
that vegetative cells are of greater importance when con—

cerned with communicable diseases. However, air—borne

4

contamination of a processed food by spores is of equal
importance, since the conditions are usually ideal for

germination.

2.1b Sedimentation and Deposit

An air—borne microorganism is subjected to the
influence of gravity and the motion of the surrounding
fluid. Most evidence (Decker, et_al:, 1962) indicates
that air-borne microorganisms, other than viruses, are 0.3
micron in diameter or larger. According to Wells (1955),
particles of this size will settle from the air in a manner
described by Stokes's law. Tanner (1963) and DallaVallo
(1948) express this law as:

(9 —ng) s dzc

 

vg -. P 91817 (2.1)
where:
vg = terminal velocity of aerosol particles
pp = density of aerosol particles
pg = density of air,
g = gravitational constant
d = diameter of aerosol particles
u = viscosity of air

The Cunningham "slip" correction factor (0) is prOportional
to the mean free path of the gas molecules and becomes
increasingly important for particles less than 20 microns

in diameter. Tanner (1963) discusses the difference between

quiescent and turbulent aerosols and indicates that Stokes

equation (2.1) will apply in both conditions. In general,
a quiescent aerosol will "fall-out” at the constant rate
of particle fall described by Stoke's equation (2.1). A
turbulent aerosol possesses a constant rate of fallout of
particles, which is prOportional to the rate of particle
fall (vg) and the aerosol concentration. Tanner (1963)
assumes that deposit on walls and ceiling of a chamber is
negligible, and develOped the following equation for

evanescence of a quiescent aerosol:

C v t .
(5) =1- a.— M
O Q

Both Wells (1955) and Tanner (1963) described the sedimen-

tation of a turbulent aerosol as:

(C) ( V—E—t) ( >
— = 1 - exp - 2.3

where:

C = concentration of aerosol at any time, t

CO = concentration of aerosol at t = O.
vg = terminal velocity of aerosol particles.
h = height of aerosol chamber

The fact that aerosol particles will deposit when
subjected to certain conditions is demonstrated by Porter,
et a1. (1963) while studying the decay of an aerosol
moving through a duct. Experimental results indicated that
this decay or deposit was a function of particle size,

velocity and duct size.

2.10 Viabiligy

 

Although some air—borne spores may have nearly
unlimited Viability, the viability of a vegetative cell
will be limited depending on the conditions to which it
is exposed. The death of vegetative cells is expressed

by Wells (1955) in the following manner:

Ln <%—>= —Kt (2.4)
.0
where:
K = death rate constant
t = time

Here the death rate constant (K) is dependent on many
factors such as bacterial species, air temperature and
relative humidity.

The factors affecting the viability of air-borne
bacteria have been studied in detail by Webb (1959).
When aerosols consisted of bacterial cells from distilled
water, the death of the cells appeared to occur in two
stages; rapid loss in viability during the first second
followed by a slower death rate which obeyed first order
kinetics at low relative humidities. The results suggested
that death of the cells resulted from movement of water
molecules in and out of the cell, in an equilibrium system,
resulting in a collapse of the natural structure of cellular
protein. Wells (1955) indicated that, in general, the
initial death rate is higher in dry air, but longevity of

survivors appears to be greater in dry air than in moist air.

Experimental determination of death rate constants
was conducted by Kethley, et a1. (1957) for bacterial

aerosols of Serratia marcescens. The determinations were

 

made in an aerosol chamber and by use of equation (2.4).

The results obtained are presented in Table 2.1

TABLE 2.1.--Influence of relative humidity on death rate
constants of Serratia marcescens.

 

 

 

 

 

 

Washed Cells Cells Dispersed from
Dispersed from Water 0.3% Beef Extract Broth
Relative
Humidity Ave. K S. E. Ave. K S. E.
% (l/min) (l/min)
16 0.021 0.0008
20 0.032 0.0020 0.020 0.0050
25 0.040 0.0010 0.020
40 0.060 0.0030 0.025
52 0.025 0.0003
60 0.044 0.0020 0.032 0.0020
80 0.008 0.0003
90 0.036 0.0020
95 0.021 0.0010

 

The results (Table 2.1) illustrate the influence of

relative humidity on death rate constants for Serratia

 

marcescens dispersed from different types cd' aqueous'nmdia.

 

The types of media were selected to represent the conditions

KO

surrounding an air-borne bacteria. The results indicate
that the maximum death rate for both plain bacterial cells
and cells surrounded by proteinaceous material occurs
between 40 and 60% relative humidity. However, it is
evident thatcmfljjsdispersed from beef extract broth had
lower death rates thancxiKHSdispersed from distilled
water, indicating a protective influence of the material

surrounding the cell.

2-1d flew

The methods available for sampling air—borne micro-
organisms are very similar to those used for other air-
borne particles. According to Wolf, et_al, (1959), the
methods can be grouped as follows: (a) impingement in
liquids, (b) impaction on solid surfaces, (c) filtration,
(d) sedimentation, (e) centrifugation, (3) electrostatic
precipitation and (g) thermal precipitation. All methods
used for air—borne particles must be modified to allow
for recovery of living biological particles.

The methods for sampling and evaluation of air—
borne biological particles are discussed by Wolf, gtual.
(1959). In general, methods employing the impingement
on liquid principle have very high efficiencies for
collecting and enumerating the bacterial cell suspended
in air. However, high impingement velocities may result

in losses of viability of vegetative cells. Methods

10

which sample air by use of filtration will provide collection
efficiencies as high as the efficiency of the filter media.
The methods tend to be somewhat more suitable for spores

and other resistant microbial forms since vegetative cells
may not resist desiccation associated with filter collection.

Sedimentation is probably the most inexpensive and
simple method for determining the microbiological quality
of air. However, the method has the serious disadvantage
of being selective for larger air—borne particles and not
the entire particle—size distribution. In addition, the
influence of air movement prevents an accurate correction
of this factor. For the results obtained by the sedimenta-
tion technique to be of quantitative value, the aerosol
must be allowed to settle quiescently onto a collecting
surface in a closed container. Due to the long periods
of time required for settling, vegetative cells lose
viability before reaching the surface.

Centrifugation was one of the first successful
methods develOped for quantitatively evaluating air-borne
bacterial populations (Wells, 1933). Although the effic-
iency may be very high, it is dependent on Operating
conditions and particle size. Two of the more complex
sampling methods described by Wolf, gt_al. (1959) are the
electrostatic and thermal precipitation samplers. The
electrostatic unit provides high collection efficiency at

relatively high sampling rates, but the instrument is

11

complex and requires careful attention to maintain accuracy.
Thermal precipitation samplers are complex also and
sampling rates are very low.

Wolf, et;al. (1959) describes impaction samplers as
best adapted to determining the concentration of particles
which contain bacterial cells. One of the impaction
samplers commonly used is the slit sampler which allows
collection of the viable particles on an agar surface.
Bourdillon, g£_al. (1941) found the slit samplers to be
highly efficient for the smallest bacteria-carrying
particles, under the proper conditions (air flow, slit
width, and distance of slit from surface).

2.2 Production and Study of Uniform
Bacterial Aerosols

 

 

To study the characteristics of a bacterial aerosol,
two factors are desirable: (a) production of bacterial
particles which are similar to those normally present in
airvborne populations and (b) control of aerosol concen—

tration and distribution by using an aerosol chamber.

2.2a Production of the Aerosol

 

According to Greene (1965), it is impo ible to

(.11
()1

experimentally produce an aerosol which simulates normal
conditions because of the manner in which air—borne micro-
organisms normally exist. Decker, et a1. (1962) reviews

methods used to produce bacterial aerosols such as small

12

glass or plastic atomizers. With such devices, it is
possible to produce aerosols containing a high percentage
of particles approximately 1 micron in diameter. Wells
(1955) points out that production of an aerosol involves
two stages: (a) atomization involving the formation of
liquid droplets containing bacterial cells and/or associate
particles and (b) evaporation of the liquid as described

by Raoult's Law. Although Greene (1965) indicated that
more experimental work is being conducted using lyOphilized
culture powders, Kethley, et_al, (1956) and Porter, et_al,
(1963) have had reasonable success by atomizing liquid
cultures into a prechamber. The prechamber provided con-
ditions for evaporation of liquid portion of the particles
and sedimentation of large particles. Using this technique,

with 0.3% beef extract culture media, Kethley, et a1. (19 6)

\J I

were able to produce aerosols with average particle sizes
ranging from 1.8 microns at 25% relative humidity to 2.3
microns at 80% relative humidity. The aerosol contained
particles which had no more than two bacterial cells with
90% of the particles containing only one cell. Porter,
394a1. (1963) reported experiments with aerosols which con-
tained between 1 and 8 microns when using similar techniques.
In general, Kethley, e£_al, (1957) concluded that aerosol
particle sizes could be predicted on the basis of the
atomized drOplet volume, the concentration of solids or
low vapor pressure liquids in the dispersed media and the

response of the components to relative humidity.

13

2.2b The Aerosol Chamber

 

The more prevalent and well-known uses of aerosol
chambers include the study of air-borne infection (Druett
and May, 1952; Henderson, 1952; Laurell, g£_al., (1949;
Leif and Krueger, 1950; Robertson, 91:31., 1946; Rosebury,
1947; Urban, 1954; Weiss and Stegeler, 1952) and the effec-
tiveness of various germicidal agents (DeOme et al., 1944);
Kaye, 1949; Mackay, 1952; Rentschler, 1942; Twort, gE;al.,
1940) However, chambers designed for the mentioned pur-
poses are not well adapted for studying the nature and
composition of bacterial aerosols during long time trials.
A chamber which is well suited to the latter purpose was
designed by Kethley, et_al. (1956). Experimental results
indicated that the chamber designed would allow an
increase in aerosol concentration according to the standard

ventilation equation (Silver, 1946):

C = CO [1 — exp (- 2%)] (2.5)

and would produce disappearance of the aerosol by a

similar equation:

C = C0 [exp (— $91)] (2.6)

Kethley, et a1. (1957) Proved that the aerosol concentra-
tion in the chamber was uniformly distributed by deter-
mining concentrations at points throughout the chamber.

In addition, the ability of the chamber to maintain a

l4

consistent concentration for long periods of time was tested

by sampling at intervals up to 130 minutes.

2.3 Transport Processes

 

Crank (1956) states that diffusion is the process
by which matter is transported from one part of a system
to another as a result of random molecular motions. Hinze
(1959) shows that transport of a transferable quantity
by random fluid motion is diffusive in nature. Since turbu—
lent fluid motion is a random fluid motion, the transport
of matter in a turbulent fluid must involve both molecular
and turbulent diffusion (Frenkiel, 1953). Crank (1956)
states Fick's law of diffusion as:

F = _ D 3? (2.7)

where F represents mass flux and, in the case of diffusion
due to turbulent motion, D represents the sum of the

molecular diffusion coefficient and the eddy diffusivity.

2.3a Turbulence

 

Hinze (1959) presents the following definition:
"Turbulent fluid motion is an irregular condition of flow
in which the various quantities show a random variation with
time and space coordinates, so that statistically distinct
average values can be discerned." As many authors (Hinze,
1959; Schlichting, 1960) indicate, there are distinct

differences between turbulence generated by friction forces

15

at fixed walls (wall turbulence) and that generated by the
flow of layers of fluid with different velocities past or
over one another (free turbulence).

Most frequent theoretical approaches to the study
of turbulence involves the assumption of isotropic
turbulence (Hinze, 1959; Townsend, 1956; Frenkiel, 1953).
Although this type of flow is ideal and does not exist
except under local conditions, its value is that it may
provide a fundamental basis for the study of the types of
turbulence which actually exist. According to Frenkiel
(1953) the term isotropic implies that the statistical
characteristics of the flow will be invarient under
rotation or reflection of the axes. This basic approach
to the study of turbulence was begun by Taylor (1921) and
has resulted in a definite trend toward the study of the
statistical properties of turbulence rather than the use
of phenomenological theories, which describe the influence
of mean flow only.

The term homogenious turbulence is frequently used
to describe the turbulent field in which the statistical
characteristics are not changed by translation of the axes
(Frenkiel, 1953). This type of turbulence exists in real
situations, but will form a part of a nonisotropic or aniso—
trOpic turbulence. As revealed by Hinze (1959), the contri—
butions to the theory of nonisotropic are small due to the

extreme complexity of the problem.

16

According to Townsend (1956), nonhomogenious turbulent
flow exists primarily in the following: (a) in the boundary
regions between a field of homogenious turbulence and an
adjacent undisturbed field, (b) when turbulent intensities
and other quantities are symmetrical about a plane and (c)
when turbulent intensities and other quantities are axisym-
metric. As would be expected, theoretical development of

inhomogenious turbulence is at an early stage.

2.3b Turbulent Diffusion

 

The basic transport mechanisms of momentum, heat
and mass in turbulent flow are very similar. According
to Pasquill (1962), the theoretical treatment of the
turbulent diffusion of these quantities has proceded
according to two approaches: (a) transfer theory in
which the transport rate is proportional to a concentration
gradient with a prOportionality factor or constant and (b)
statistical description in which an analytical technique
for representing the history of the fluid elements in terms
of the statistical prOperties of the turbulent motion is
used. Schlichting (1960) points out that the first approach
(transfer theory) involves calculations based on empirical
hypothesis which endeavors to establish a relationship
between the Reynold's stresses produced by mixing motions,
and the mean values of the velocity components together

with suitable hypothesis concerning heat and mass transfer.

17

According to Hinze (1959), the more complete and correct
solution to turbulent flow problems can be obtained by
expressing the turbulent-transport rate of the transferable
quantity completely in terms of statistical functions of
the turbulent velocity field and of boundary or initial
conditions.

The basic concepts of transfer theory in turbulent
flow were introduced by Boussinesq (1877) who described
Reynold's stress in turbulent flow by:

_ au-
Tt — AT -—-— (2.8)

:<;

where AT is called a mixing coefficient which is dependent
on the mean velocity. A similar relationship for transfer
of mass in turbulent flow:

a;

F = - 3 K —§ (2-9)

was prOposed by Pasquill (1962), with K equal to the pro-
portionality constant and 3% equal to the concentration
gradient. In order to use the preceding equations, it is
necessary to have knowledge of the manner with which the
coefficients vary with the mean velocity or other measure—
able quantity. One of the most useful concepts in the
description of turbulent-transport processes is the "mixing

length" theory introduced by Prandtl (1925). Prandtl‘s

mixing length hypothesis is:

du
= 2 __ —

18

where T is shear stress and A is a mixing length described
as the distance in the transverse direction which must be
covered byznlagglomeration of fluid particles traveling
with its original mean velocity in order to make the
difference between its velocity and the velocity in the

new lamina equal to the mean transverse fluctuation in tur-
bulent flow. As indicated by Hinze (1959), the "mixing
length" does not describe turbulent flow entirely correctly
but does provide a useful tool for calculation purposes.

A second and similar transfer theory was introduced
by Taylor (1915). This second theory differs from Prandtl's
momentum transport theory in that it describes the diffusion
of vorticity rather than momentum. Schlichting (1960)
indicates that this theory has particular application in
free turbulent flow. Taylor (1932) has shown that the
momentum transport and vorticity transport theories agree
when turbulent motion is two—dimensional and confined to
the plane perpendicular to the mean motion. However, when
turbulent motion and mean motion are confined to two-dimen—
sions, the results of the two theories differ significantly.
The differences between the two theories are evident again
when comparing velocity and temperature or concentration
distributions in wakes or free turbulent mixing regions.

The momentum transport theory would predict the distribu-

tions to be identical. Taylor's vorticity transport theory

l9

predicts different distributions which have been confirmed
experimentally by Fage and Falkner (1932).

If the turbulent flow is assumed homogenious and
isotrOpic, solutions to the parabolic equation of diffusion

become: very useful. This equation, as presented by Pasquill

(1962),

19:2. LC _3_ 9.9 .‘L .22

at 3x (xx 3x + By <§y 8y) + 32 (32 82) (2°11)
with Kx’ Ky, Kz equal to eddy diffusivities in various

coordinates, can be adapted and solved for a given set of
conditions. Several such solutions for point or line
sources of concentration are presented by Frenkiel (1953)
and Hinze (1959).

Experimental investigations involving turbulence and
turbulent diffusion have been concerned mainly with the
description of eddy diffusivities in terms of mean flow.
Towle and Sherwood (1939) determined eddy diffusivities
for turbulent flow in ducts and found that values increased
prOportionately to Reynolds' number. In addition, the
results indicated that the scale of turbulence in free
duct flow is significantly larger than that produced by a
grid. Results presented by Sherwood and Woertz (1939)
show that the eddy diffusivity is essentially constant
over the central portion of a turbulent gas stream in a
duct. The product of eddy diffusivity and gas density

was found to be about 1.6 times larger than the eddy

20

viscosity. A semi-theoretical relationship was established
relating the eddy diffusivity to mean velocity, duct radius
and the friction factor. The importance of having knowledge
of the scale of turbulence is revealed in investigations
by Kalinske and Pien (1944). Results revealed that the
eddy diffusivity is directly related to the scale of
turbulence, which must be measured to provide an accurate
prediction of the turbulent diffusion.

A statistical description of the turbulent field
is required in order to accurately solve a turbulent
transport problem. The basic concepts involved in statis—
tical theory of turbulence were introduced by Taylor (1921)
and develOped by Taylor (1935). In general, the statistical
Concept involves the correlation between the velocity of
a particle at one time and that of the same particle at a
later time, or the correlation between simultaneous
velocities at two fixed points.

Statistical aspects of turbulent flow are reviewed
by Frenkiel (1953), Hinze (1959), and Pasquill (1962).
Basically, turbulent flow cannot be described by a mean
velocity, only,since the velocity fluctuationsaround the
mean velocity are an indication of the intensity of turbu-
lence. Usually, the instantaneous velocity is represented
by:

u = E + u' (2'12)

21

where u' represents the turbulent velocity or instantaneous
difference from the time mean velocity J and such that

ET = 0. However, since the turbulent velocity changes
continuously with time, Dryden and Kuethe (1930) suggested
the use of the root mean square value /:?§_ . The intensity

of turbulence, degree of turbulence or turbulence level is

(13—?! >16

then defined as for the longitudinal direction and

_ u

L
W”)2
————— would be the transverse intensity of turbulence.

Turbulent transport processes may be statistically

described in two ways according to Hinze (1959). The
Eulerian description involves the variation of some pro-
perty with respect to a fixed coordinate system. The
variation of the property connected with a given fluid
particle or fluid lump while moving through the flow field
is the Lagrangian description. Frenkiel (1953) defines

the Eulerian longintudinal correlation coefficient for

velocity as:

 

RX(x) = i Q (2.13)
we ““th

The value of this correlation coefficient will range from
one when the points (P and Q) coincide to zero when the
points are far apart. A similar correlation coefficient

can be calculated in the transverse direction. The Eulerian

time correlation coefficient would be defined as:

22

 

u'(t) u'(t+h)
R (h) = p . P
‘3 /u"p"'" (It)? /u£) (t+h) 2

 

(2.14)

 

where h represents the time lag between instantaneous
velocities at the same point.
Frenkiel (1953) defines the Lagrangian correlation

coefficient in the longitudinal direction as:

 

u uA(t7 uA(t+h)
RtL(h) = (2-15)
/uA(t)2 /uA(t+h)2

 

This correlation coefficient corresponds to a Lagrangian

time—scale of turbulence:

u w u :
LtL = f RtL (a) d a (2.16)
O

A similar Lagrangian length-scale of turbulence can be
calculated based on the distance traveled during time (h).
According to Taylor (1935) this length is analogous to
Prandtl‘s mixing length. The corresponding Eulerian
length-scale is an indication of the average eddy size.
Additional description of turbulent flow is obtained
by determination of the spectrum which measures the relative
contribution of various frequencies of velocity fluctuations
to turbulent energy. Frenkiel (1953) defines the longitudinal

Spectrum of turbulence as:

Fx(k') =

elm

577' /{ Rx(s) cos (k's) ds (2.17)
o

23

where the functiOn [Fx(k')] represents the contribution to
577 at the wave number k'.

The dispersion of a fluid element or particle in
turbulent flow is usually iescribed in terms of the
variance of the coordinate system components (f7, if; or 2?).
Assuming homogenious isotrOpic turbulence, Frenkiel (1953)
derived the fundamental equation of turbulent diffusion:

‘7' ‘2' t
y = 2 v of (t-a) Rh (a) d a (2.18)

(a).

where a is equal to time lag used for calculating Rh
When dispersion time is large compared to the Lagrangian
time-scale of turbulence (equation 2.16) the correlation
coefficient becomes very small and equation 2.18 becomes:

37’2" ~ 2 \77 Lht (2.19)

If dispersion time is small compared to the Lagrangian

time-scale (Lh)’ Frenkiel (1953) has derived the expression:

~ 2
yr: [1-1.2: :‘Vztz (2.20)
h

or when dispersion time is small compared to the microscale

of turbulence Ah:

577 = \72' t2 (2.21)
For the case when dispersion time neither large nor
small compared the Lagrangian time-scale, Frenkiel (1953)

introduces a dispersion factor:

24
_ 1 -—

Further description of the turbulent flow involves
representing the correlation curve by known functions.

If vt = v7'Lh and dispersion time is large, equation
2.19 becomes:

§7 = 2vtt (2.23)
and the eddy diffusion (Dt) becomes:

D = v + v (2.24)

when the molecular diffusivity coefficient is assumed equal
to the kinematic viscosity.
Frenkiel (1953) defines a factor of turbulent

diffusion:
_T
n = 2 d(dt) = ‘77 Uj/t Rh (a) d a (2.25)

By replacing the constant eddy diffusivity in the
diffusion equation with the above factor (n), the equation
becomes valid for a large number of dispersion times
(Pasquill, 1962).

Since Fick's diffusion equation is not valid even
in homogenious isotropic turbulence, experimental eddy
diffusivities obtained in this manner can only represent
apparent coefficients for conditions studied. Frenkiel
(1953) explains that the ratio of the apparent coefficient
to the real eddy diffusivity is related to the statistical

properties of the turbulence:

25

U
51)
Inf
,4
N

- ° ‘ (2.26)

U
C

N
._3

The ratio is then a function of relative dispersion time

(T = t/Lh) and shape of the Lagrangian correlation curve.

2.3c Transport in Mixing Regions

 

Typical examples of free turbulent flow and the
corresponding mixing which occurs are reviewed by Schlichting
(1960). A free jet boundary occurs between two streams
which are moving at different speeds in the same direction.
A free jet occurs when a fluid is discharged from a nozzle
or orifice. The turbulent region behind a solid body
moving through a fluid or a solid body in a stream of air
is called a wake. These types of free turbulent flow can
be described by boundary layer equations which have been
solved for various sets of conditions by Schlichting (1960)
and Pai (1954).

A basic requirement for the description and solution
of turbulent mixing problems is knowledge of the velocity
distribution. Goldstein (1930) provided a detailed solution
to the boundary layer equations for two-dimensional steady
motion. Howarth (1934) and Tomotika (1938) used the
vorticity transfer theory to describe the velocity distri—
bution in plane and axially symmetrical jets. Results
revealed an identical distribution when compared to momentum
transfer theory, but the authors concluded that experimental

temperature distributions would be required to test both

26

theories. Kuethe (1935) assumed that Prandtl's mixing
length is proportional to the breadth of the turbulent
mixing region and obtained solutions for velocity fields
for mixing of two parallel streams of different velocities
and for an axially symmetrical jet. Albertson, et_al.
(1948) used three assumptions to solve for the flow pattern
in a submerged jet. The assumptions were: (a) the pressure
is hydrostatically distributed throughout the flow; (b)

the diffusion process is dynamically similar under all
conditions; and (c) the longitudinal component of velocity
within the diffusion region varies according to the normal
probability function at each cross section. Experimental
results indicated validity of the assumptions. Pai (1949)
solved the equation of motion for the mixing region of a
two—dimensional jet and obtained a solution containing the
Gaussian error function. Lock (1951) obtained solutions
for the velocity distribution in the laminar boundary

layer between two parallel streams which differ in density
and viscosity. Results indicated that the solutions depend
on the ratio of the velocities of the two streams and the
product of the viscosity and density ratios. Torda, et_al.
(1953) used the von Karman integral concept to analyze

the turbulent incompressible symmetric mixing of two
parallel streams. The velocity distribution in the mixing
region and the thickness of the region was evaluated while

accounting for the influence of the upstream boundary layers.

27

Pai (1955) solved the equations for two—dimensional and
axially symmetrical turbulent jet mixing of two gases at
constant temperature assuming constant exchange coefficients
in the mixing region.

A second essential requirement for study and descrip—
tion of turbulent transport of quantities other than
momentum is the concentration distribution. The concentra-
tion distribution for a circular jet with annular coaxial
stream was measured by Forstall and Shapiro (1950). The
results indicated that concentration diffuses more rapidly
than momentum. Pai (1954) compared theoretical equations
with experimental results and indicated that for mixing
regions far downstream, the concentration profiles can be
represented by error functions. Pai (1956) presented
solutions to laminar jet mixing problems for velocity,
temperature, and concentration distributions. In general,
all solutions contain some form of the error function.
Batchelor (1957) discusses the statistical characteristics
of diffusion in jets, wakes, and mixing layers. The
author's hypothesis is that the velocity of a fluid particle
in free turbulent shear flow exhibits a corresponding
Lagrangian similarity and can be transformed to a stationary
random function” Csanady (1963) solved a differential
equation derived from the energy balance of the mixing layer
and obtained solutions for turbulent intensity profiles

which agreed with experiments.

28

Several investigations have dealt specifically with
velocity and concentration distributions in mixing regions
created by wakes. Goldstein (1933) presented the calcula-
tions of the velocity distribution in the wake behind an
infinitely thin plate parallel to a fluid stream. Holling-
dale (1940) and Townsend (1949) have presented theoretical
and experimental results which describe velocity distribu—
tions and transport in the wake mixing regions. The
validity of the mixing length theory for turbulent shear
flow has been questioned. Experimental results, reviewed
by Batchelor (1950) presents general mechanisms for
transfer of momentum, turbulent energy and heat. However,
analytical theory corresponding to the experimental results
has not been formulated. Cheng and Kovitz (1958) present
solutions to the initial value problem involving mixing
and chemical reaction in a laminar wake of a flat plate.
Coles (1956) proposes the use of universal flows to
describe the mean velocity profile of two—dimensional
incompressible turbulent boundary layer flows. The wake
model for free-streamline flow is used by Wu (1962) to
treat the two-dimension flow past an obstacle with wake

or cavity formation.

3. THEORETICAL CONSIDERATIONS

The transport of air—borne bacteria through an
Opening between two rooms with different concentrations
probably involves many mechanisms acting individually
or simultaneously. For purposes of this investigation, a
theoretical mixing region model will be proposed. The
model consists of two different uniform concentrations
of air—borne bacteria separated by a partition. The
two-dimensional mixing region is located at an Opening in
the partition through which transport of the aerosol
occurs. The opening is considered infinitely long in
the direction perpendicular to air flow past both sides.
The mechanism of transport considered is the turbulent
dispersion of the high concentration aerosol into the
low concentration air and the subsequent entrainment on
the low concentration side of the model. The analysis
of the model involves consideration of several factors:

a. Equal air flow on both sides of the mode1—-this

analysis will involve determination of disper-
sion in highly turbulent air moving at low flow
rates typical of ventilation systems. Depending
on the intensity of turbulence in the free
stream, the influence of turbulence created by

a wake of the partition may need to be considered.

29

30

b. Unequal air flow across the mixing region-~a
complete analysis of this case involves several
considerations. Due to unequal flow, the
possibilities of momentum transport through the
mixing region and variation of turbulence across
the mixing region must be taken into account.

c. Variation in Opening size-—the height of opening
in the same direction as the air flow will have
a direct influence on the extent of dispersion.
In addition, any influence of opening size on
turbulence characteristics should be established.

d. Width of partition-—the width of the partition
at the initial point of mixing will require at
least two considerations. One is the possibility
of increased turbulence due to the wake. The
other is a reduction in dispersion length due to
the increased width at the initial point of
mixing.

e. Temperature gradient-—the primary considerations
involving temperature gradient are the influence
on viability of the aerosol and the possibility
of increased convective currents.

In order to allow an analysis which lends itself

to mathematical ease and clarity, several assumptions are

required:

31

a. The particle size of the bacterial aerosol is
uniform, ige., the influence of transport mecha-'
nisms and gravitational forces is the same for
all particles.

b. The die—away characteristics of all particles
in the aerosol are uniform.

c. The influence of a mean pressure gradient
existing at the opening is negligible.

d. Transport due to molecular effects is very small
compared to turbulent transport, i.e., Brownian
motion is negligible.

e. Turbulence in the mixing region is isotropic,
i.e., G77'= VT? = W77.

f. The differences in temperature encountered are
sufficiently small to allow the use of constant
fluid properties.

The first two assumptions are based on work conducted

by Kethley, g§_al. (1956) with experimentally generated

Serratia marcescens. These assumptions would rarely apply

 

under actual conditions, but they are necessary simplifying
assumptions which can be met experimentally. The third,
fourth and fifth assumptions depend primarily on the inten—
sity of turbulence which exists in the mixing region. The
model specifies sufficient turbulence to maintain uniform
aerosol concentrations on both sides of the partition;

therefore, the indicated assumptions would appear to be

32

good. Since a 20°F. temperature gradient will produce less
'than fivecper cent change in the prOperties of air, the

last assumption can be used without major concern.

 

3.1 Basic Diffusion Equations

The two-dimensional mixing region described in the
model is not unlike the laminar or turbulent jet boundary
described frequently in fluid mechanics literature. In
most cases, the mixing region formed by the two parallel
streams is treated as a boundary layer and the same simpli—
fying assumptions to the basic equations are adopted
(Schlichting, 1960). Using this approach the transport in
the mixing region model can be described by the following
steady—flow equations:

a. Equation of motion:

—-afi —- 35 ._ 323
u 3; + v _§ - V By: (3.1)

b. Equation of turbulent energy:

 

— aui2 -— au'2 _ au'z
uax +VW‘VIW (33)

c. Equation of diffusion:

— 3C — ac _ 326
u 3X +V ~53,- -Da§—)7Y (3-3)

d. Equation of energy:

— ae — 58 _ 329
u-a—X' + V W - at??? (30“)

e. Equation of continuity:

33 av _
.32. +53; -0 (3-5)

33

These equations should completely describe the turbulent
transport of aerosol particles in the model proposed. The
solution to the equation of motion will describe changes
in mean velocity across the mixing region when unequal air
flows are analyzed. The very low magnitudes of the mean
air velocity and small differences in mean air velocity
between the two sides should allow treatment of the mixing
region as a laminar jet boundary and the use of known
fluid properties for air.

The prOposed model requires sufficient turbulence
to maintain homogeneous concentrations on both sides of
the mixing region. This turbulence must be superimposed
on the low mean velocities which exist, and therefore
moves slowly past the mixing region. The proposed equation
of turbulent energy describes the distribution of the
statistical turbulent energy factor (J77). This distribu-
tion becomes particularly important in cases where a
gradient of the turbulent energy exists across the mixing
region model.

The equations of diffusion and energy are prOposed
in order to describe distributions of concentration and
temperature in the model mixing region. Because the pro-
posed model considers only transport due to turbulent
effects, the constants, Da and a will be referred to as

t
apparent eddy diffusivity and turbulent thermal diffusivity,

34

respectively. The continuity equation specifies that con—
servation of mass exists in the mixing region.

The purpose of the proposed mixing region model is
to provide some theoretical basis for the transport of a
bacterial aerosol through an opening in a partition
separating two different concentrations. To provide mathe—
matical ease in the description of this transport, it
would be desirable to Obtain closed solutions to the equa-
tions which represent the distribution of the various
parameters in the mixing region. One approach to attaining
this objective is to make additional assumptions with
respect to flow conditions in the mixing region. The
assumption that V = 0 should be valid based on specifi—
cations of the model. As indicated, the overall movement
of air past the Opening is in the downward (+x) direction.

All other components of air movement are turbulent fluctua—

tions. Therefore, the only non-negative mean velocity is
u (x—component). The assumption that v = 0 simplifies the

previous equations considerably and thus they may be stated

in the following manner:

a. Equation of motion:
—aJ _ ‘325
1.1—; - \z W (3.6)

b. Equation of turbulent energy:

"311,2 5213—17-
ax t ayz

 

(3.7)

 

35

0. Equation of diffusion:

- 19 = 320

u 8x Da 5;? (3.8)
d. Equation of energy:

—-39 _ 329

u 53? ‘ “t W (39)

The equations of interest are now reduced to more
simple forms similar to the heat conduction equation.
Such equations have been used frequently by Pai (1949, 1955,
1956) to obtain solutions which describe velocity distri—
butions in laminar and turbulent jet mixing regions.

More firm support for the use of the preceding
equations in regions of free turbulence was provided by
Reichardt (1941, 1944). Reichardt's inductive theory of
turbulence is derived almost completely from experimental
evidence, which indicates that velocity profiles in free
turbulent flows can be approximated very successfully by
the Gaussian error function. Reichardt's fundamental
equation for describing the velocity distribution in free

turbulent flow is:

au“z 32.32 ( .
3X _ A(X) ayz .3-10)
where A is a momentum transfer length. The similarity of

Reichardt's equation and equations preposed for use in
this investigation is apparent.
Solutions to equations 3.6, 3.7, 3.8, and 3.9 can

be obtained by use of boundary conditions which describe

,1

3b

the model mixing region. These boundary conditions can be
stated as follows:

At x = 0, y > 0:

— = —— ‘77 = ‘T? c = c =

u uL, u uL , L e 6L (3.11)
x > 0, y —+ 0o:

— = __ —77 = —TT = =

u uL, u uL , C CL, 6 6L (3.12)
x > 0, y —+ —w:

— = —— _TT = —TT = . =

u uH, u uH , C QH’ e 6H (3.13)

 

 

 

“'— 12 '2
u —u u -u
—=— H L 72:72" H L C=
u u. + 2 , u uL + 2 , %,
C -C 6 -6
+ H L , e: 8L+ H2L (3.114)

These boundary conditions lead to the following solutions
(See Appendix A.2) to the proposed equations:

a. Equation of motion:

= % 1 - erf % uL (3.15)

VX

$1 cl
L—1

J
U_
H

b. Equation of turbulent energy:

uv2_u12 -' fif-
~ _ 1 .y / L

 

H L

c. Equation of diffusion:

C - C
L I
———————— = 1 — erf L (3.17)
CH ’ CL 2 Dax

[UH-J

 

37

d. Equation of energy:

a -e /u—
L y L
317;“ ‘ l ’ “TC at x (3‘18)

 

I\)|I—‘

H L

The above solutions contain the error function which
is typical of solutions to the heat conduction equation.
Several workers (Reichardt, 1944; Albertson, 1948, Liepmann
and Laufer, 1947; Corrsin, 1943; Hinze, §t_al,, 1948;
Schlichting, 1960 and Forstall and Shapiro, 1950) have
presented experimental results which confirm that velocity,
temperature, and concentration distributions in jet boun—
daries and wakes can be represented by solutions containing

error functions.

3.2 Turbulent Diffusion

 

A complete description of the transport in the model
mixing region depends on an accurate determination of the
air flow conditions. Since turbulence is the primary
mechanism of concern, the statistical description introduced
by Taylor (1921) offers the most accurate approach.

The following derivation of the fundamental equation
of turbulent diffusion should apply to the model mixing
region proposed in this investigation. For transport of
the bacterial aerosol to occur in the model mixing region,
the particles must move in a direction perpendicular to
the opening (y-direction). The y-location of a given

particle after a dispersion time of t would be:

38

t
y = / V'(E) d a (3.19)

o
where 5 represents the time lag between instantaneous
velocity measurements. By computing the variance of the

y-component of particle location:

 

t 2 t
I7= / V'(€) d 5:] = [ V'(t) V‘(€) d5 (3.20)

O O '

and consideration of the auto correlation coefficient:

 

 

 

_ V'(tI V'Ig)
Rug) - v (3.21)
then:
t t
/ v'(t7 v'n) d5 =57? / Rd.) at (3.22)
O 0

By integration of the left side of equation 3.22

ET??? // NTTEI d6 = v' t) y = VT? /[ R(£) 95
o o

(3.23)

By restating:

‘T“a l d [‘E] - '77" /[t R( ) d ( 24)

V y 2 a? y ' V O E.» E 3.
then:

T t
'y‘T= 2 W / / Rm dadt (3.25)
o o

which is the fundamental equation of turbulent diffusion
first derived by Taylor (1921). This expression provides

an accurate and direct method of determining the statistical

39

dispersion of the bacterial aerosol through the Opening into
the low concentration air. This information is attainable

by determination of a turbulent energy factor (577) and auto—
correlation coefficients, both of which can be obtained by

measurement of instantaneous velocity fluctuations.

3.3 Turbulent Transport Coefficient

 

The transport of the bacterial aerosol through the
experimental opening will be presented as a turbulent
transfer coefficient. This coefficient is based on Fick‘s

law of diffusion (Treybal, 1955):

A a

O

(3.26)

I
II
I
U
I

3>
O)

y

which describes the movement of some component due to a
concentration gradient. The mass flux (NA) represents

the rate of movement and D is the proportionality constant
or diffusion coefficient. When describing turbulent
diffusion, such as in this investigation, the equation is

written as:

A :_D 8—C.

A t 3y (3-27)

where Dt is the eddy diffusivity.

40

The mixing region model and the corresponding trans-
port of aerosol through an opening perpendicular to the
concentration gradient, the variables of equation 3.27

can be separated in the following manner:

NA b CL
A‘ /f dy = —Dt ,/r dC (3-28)
0 c
H
where b is equal to the width of the mixing region. By

integration, equation 3.28 becomes:

NA D

77 = E} (cH - CL) (3.29)
with CH and CL being equal to the high and low concentra-
tions, respectively, the ratio (Dt/b) can then be replaced
by the transfer coefficient (kc) in the following manner:
NA = kc A(CH — CL) (3.30)
This equation describes the turbulent transport coefficient
to be used. One important factor must be recognized.
Because of the entrainment mechanism involved in the model,
this coefficient (kc) will be proportional to the mixing
region width and will not decrease as suggested in equation
3.29. However, the relationship of the coefficient to the
mass flux (NA)’ area (A) and concentration gradient
(CH — CL) remains. Therefore, the turbulent transfer
coefficient (kc) is excellent parameter to be measured

experimentally in this investigation.

41

3.4 Eddy Diffusivity

 

Transport in the model mixing region occurs only
due to turbulence as specified by basic assumptions in the
description of the model. As indicated by equation 3.27,
turbulent diffusion is described in terms of an eddy
diffusivity Dt which is analogous to the diffusion coef—
ficient in molecular diffusion. However, a basic differ-
ence does exist in that the molecular diffusivity is
characteristic of the fluid in which diffusion occurs,
whereas the eddy diffusivity is related more closely to
the flow cOnditions which exist. Because of this differ-
ence, it will be necessary to determine an eddy diffusivity
which corresponds to each set of flow conditions investi—
gated.

The most desirable method for determining eddy
diffusivities in the mixing region model would be by
measurement of concentrations at points in the mixing
region and use of equation 3.17. However, this approach,
is time consuming and would not provide the accuracy
desired because of difficulties encountered in making
point concentration measurements of bacterial aerosols.
The statistical approach proposed by Taylor (1935) offers
an alternative method. From the definition of the auto-
correlation coefficient in equation 3.21, it is evident
that the coefficient is unity at E = 0 and zero at E —+ w

Because of this relationship, it is possible to define some

time (T) beyond which R(g) = 0. Then, it is possible to

state equation 3.23 as:
___ t
yV' = V'2 // R (5) d5 (3.31)
o

where yv' is constant for t > T even though y? is increasing
continuously. For these conditions, the constant (yv') is

defined as the eddy diffusivity:

t
Dt = 677' /f R<£> dé (3.32)

o

which is constant for a given turbulent energy factor

(577) and integral of the autocorrelation coefficient.
In addition, Taylor (1935) defines a ”length scale

of turbulence" as:

1 't
‘3«(({7_—'_7)/2 = V77. // 3(5) d6 (3.33)
O

01"

1’ t -
2, = (777)? I R(g) d5; (33“)
O

This length scale is assumed to have the same relation to
turbulent diffusion as the mean free path does in molecular
diffusion. This value may provide considerable information
on the mechanism of transfer for the mixing region model

of this investigation.

3.5 Transport in the Mixing Region

 

For purposes of this investigation, transport of

the bacterial aerosol from the high concentration region

43

to the low concentration region will occur due to disper-
sion in the mixing region and entrainment on the low
concentration side. Equation 3.25 describes the extent
of dispersion in the direction perpendicular to the
Opening and (577)15 should then represent the width of the
mixing region on the low concentration side. The entrain-
ment of the aerosol would occur due to the mean flow of
air along the low concentration side.

If the dispersion time (t) is large compared to the
time (T) required for R(£)—+ 0, then equation 3.25 can be

stated as:

T t ,/
I?" = 2V” of 13(5) d5 / dt = 2(FTV 2.1: (3.35)
O

For turbulence sufficient to maintain uniform aerosol
concentrations, such as specified for in the mixing region
model, dispersion time (t) should be large compared to the
time (T). For each set of flow conditions, the apparent

mixing region width can be defined as:
t L t
b = (375V = 2<v'2)2 2,t 2 (3.36)

3.5a Isovel-Isothermal Flow

 

The first case to be analyzed will be that of equal
flow through both sides of the mixing region model. The

flux of bacterial aerosol can be evaluated by:

b
NA = o/ uL C dy (3-37)

44

where:
N = the number of aerosol particles passing through
the opening per unit time.
b = the apparant width of the mixing region defined

by equation 3.36.

CI
u

mean velocity past the opening.
C = concentration of bacterial aerosol at any point
in the mixing region.

By substitution of equation 3.17 into equation 3.37:

J C b
NA = L2H / 1 — erf (g /U'L- )dy (3.38)
0 Da x

where it is assumed that CL = 0. From the definition of

the turbulent transfer coefficient:

 

k = A (3.39)

 

a = X UL (3.40)
2 D x
a
then:
EL b
k0 = 2H 6/” erfc B dy (3.41)

By rearrangement of the terms in equation 3.41, the
equation can be stated in the following dimensionless

form:

kg
r’fi
U

 

 

 

 

__s_£_ = K' fée) L t —E (3.42)
u' 2 b0 0 u 2 H vt
where:
cht
‘2 b = Dimensionless transport group (3.43)
u
GL-Vt
= Dimensionless turbulence group (3.44)
u'2 H
bO = width of partition (3.45)
H 3 height of opening. (3.46)
f(8) = I erf: B dy = ierfc(o) —ierfc (B) (3.47)
o
K' = experimental constant (3.48)

The entire transport of bacterial aerosol in the

turbulent mixing region can be described by equation 3.42

when air flows are equal.

3.5b Turbulent Mixing with Unequal Velocities

 

The second case to be considered presents a more

complex situation to analyze, since flow conditions and

parameters vary across the mixing region. Since the

dispersion length (y?) will vary across the mixing region,
the mixing region width (b) as defined in equation 3.36
will vary, also. To define this parameter in a manner
which will be repreSentative of the actual situation, the

measurement of dispersion (y?) obtained at the Opening

46

(y=o) will be used to define the mixing region width (b).

The measurements obtained at this point should represent

a mean of conditions which exist across the mixing region.
The mean velocity (3) will vary across the mixing

region, also. However, the region over which a varies

before decreasing to E

L
the mixing region (b) (See Appendix A.3). Therefore, the

is small compared to the width of

mean velocity (3:) can be used in equation 3.42 without

introducing significant error.

3.5c Influence of Partition Width

 

In order to express results obtained with variable
partition widths in the form of equation 3.42, some modifi-
cation must be introduced. The influence of a wider
partition at the initial point of mixing is to decrease
the dispersion (y?) unless additional wake effects are
introduced. For purposes of analysis, the mixing region
width will be decreased by an amount equal to the partition
width. The same expressions and relationships, as introduced

previously, can then be used.

3.5d Turbulent Mixing with a Temperature Gradient

 

Since the proposed mixing region model for bacterial
aerosol is based completely on turbulent transport, the influ-
ence of a temperature gradient across the opening is not taken

into account. Two additional factors must be considered

47

in this case: (a) the influence of temperature and relative
humidity on viability of the aerosol and (b) the influence
of a heat flux through the opening. By taking these factors

into account, an expression similar to equation 3.42 can

be used.

4. EXPERIMENTAL PROCEDURES

AND EQUIPMENT

4.1 Equipment

 

In order to attain the specific objectives of this
investigation, reasonable control of temperature and
relative humidity was required. Therefore, all experiments
were conducted in a room with an air temperature of 70° t
30F. and relative humidity of 70 i 10%. Both the dew-
point and dry-bulb temperatures were continuously recorded

by a temperature recorder (Figure 4.1).

4.1a Aerosol Chamber

 

The overall interior dimensions of the aerosol
chamber, shown schematically in Figure 4.2 were four feet
by eight feet by four feet with a partition to divide it
into two four foot cube compartments. The interior walls
were constructed of 1/4 in. tempered masonite and the
interior surfaces were finished with two coats of white
enamel before polishing to a smooth finish. The partition
contained an adjustable sheet metal section (Figure 4.3)
which was two feet in Width and could provide an opening
of up to nine in. with the bottom of the opening 12 in.

above the chamber floor.

48

49

 

 

 

 

 

III III II: III III =|I .1 ‘Ir III
40 20 -0+ 20 40 60 ,1' 100 120 140

$.25.

IIOIIIIO‘IIIIII‘

' ~u.‘ nil-21:0“.

'0

 

Figure 4.1.——Temperature and relative humidity recording
instruments.

50

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8 ”fight what

no 2<mw<5 o_._.<2w10m II . m . : opswflm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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an.» 2:38 fl
2.5.5. :9. 32.3. cum-3:81..

 

 

 

 

51

 

Figure H.3.--Partition and opening between com-
partments of aerosol chamber.

 

Figure u.u.--Air diffuser in ceiling of one
compartment of aerosol chamber.

52

The entire aerosol chamber was insulated with
Microlite insulation material (density = 3/4 1b./ft3; k =
0.25 BTU/hr. °F. in.) which was placed in the space
between the Masonite and l/N-in. plywood which formed
the exterior walls. The front of the chamber was designed
to allow easy removal and was constructed of the same material
as the rest of the chamber. Many experiments, which did
not involve heating of the air, were conducted with the
front replaced by two four foot sections of clear plexi-
glass to allow observation of the experiments.

The compartment interiors were mirror images. The
only internal projections were the ll.5-in. diameter air
diffusers, (Figure 4.“), which projected approximately
one in. from the ceiling. The floor of each compartment
contained the air outlet; a 3-in. diameter opening at the
geometric center.

During experiments, air leaving the ultra—high
efficiency air filter (American Air Filter 00.), shown
in Figure “.5 was passed through a venturi tube (Figure
u.6) to obtain an accurate measurement of air flow.
Pressure differences in the venturi tube were measured
by micromanometers (S.G., of fluid = 0.797). Bacterial
aerosol from a prechamber was injected into the air stream
and the high concentration air was uniformly distributed
throughout the high concentration compartment of the

chamber by an Anemostat CMl air diffuser (Anemostat

 

53

 

Figure U.5.—-Ultra-high efficiency air filter.

 

Figure N.6.——Venturi tube and micromanometer used for
air flow measurement.

S“

Corporation of America). Air leaving the high concentra-
tion compartment passed a copper—constantan thermocouple,
which was connected to a Brown Electronic recording
potentiometer, shown in Figure 4.1 to provide a continuous
record of air temperature. Just before the air passed
through the ultra-high efficiency filter, air samples

were collected by a Casella slit sampler (Figure 4.7)

for determination of aerosol concentration. Air was
sampled from the duct by vacuum through an isokinetic
probe (Gelman Instrument Co.)

The low concentration compartment was equipped in a
similar manner except that no aerosol was injected into
the air stream and, in some experiments, the air was
heated by a small resistance coil before entering the
chamber. The 3-in. diameter duct serving the low concen-
tration compartment was insulated with Microlite material
to prevent heat loss during experiments involving heating

of the air.

A.1b Aerosol Generation

 

The two primary parts of the aerosol generation
system were the atomizer (DeVilbiss all glass No. 40)
and the 2M-in. cubical plexiglas prechamber shown in
Figure 4.8. A clean regulated supply of compressed air
was provided to the atomizer by a pressure regulator
(C. A. Norgregn Co. Type 2A2) at a flow rate of 0.225 ft.3/

min. measured by a Brooks Rotameter Type 1110 flow meter

 

Figure u.8.-—Prechamber and related parts of
aerosol generation system.

56

at 20 lb/in2. Liquid culture was provided to the atomizer
from a 2 liter aspirator bottle (Figure A.9) used as a
reservoir. A constant supply was provided by maintaining
the proper level in the reservoir with respect to the
atomizer. The liquid aerosol then passed into the pre-
chamber where liquid portions of the droplets evaporated
and larger particles settled to the floor. This method

of aerosol generation was selected on the basis of investi-
gations by Kethley, gt_al. (1956) which indicated that
aerosol particles produced from 0.3% beef extract broth
were consistently between 1.8 and 2.3 micron and not

less than 90% of the particles carried single bacterial

cells.

A.1c. Air Sampling

 

For most experiments, air was sampled at three ports
consisting of Gelman isokinetic probes. The probes were
connected to a common sampling station (Figure 4.10) by
tygon tubing. The sampling station, which provided rapid
consecutive sampling at various ports, was in turn
connected to the Casella slit air sampler (Figure u.7).

The Casella slit air sampler includes a vacuum source

3

used to collect the samples at a rate of one ft per min.
The sampling method uses the solid impaction technique,
which involves collection of all air-borne particles on a

solidified agar surface. Air from the sampling probe

57

 

Figure A.9.——Aerosol atomizer and culture reservoir.

 

Figure A.10.--Air sampling station and point of aerosol
injection into duct.

58

passes through a 0.013 in. by one in. slit and particles
are collected on the agar surface 2 mm below the slit.
Since the petri dish, containing the agar media, is
rotating continuously; the particles are distributed
uniformly over the entire surface. Provisions for varying

the sampling period to one, two or five min. are available.

4.1d Air Velocity and Turbulence

 

Mean air velocity and intensity of turbulence were
measured using a constant current hot wire anemometer
(Model HWB No. 216 by Flow Corporation, Arlington, Mass.).
A 0.0005-in. diameter filament attached to a standard
Flow Corporation probe was used for detection.

Figure 4.11 shows the hot wire anemometer and auxilary
equipment used for turbulence measurement. The signal
from the anemometer amplifier was fed through a 7 KC low
pass filter to a Moseley X—Y recorder (Figure 4.12). The
velocity fluctuations were recorded at settings of five
volts/div. The Hickok Model 685 cathode ray oscilloscope
was used for measurement of square—wave amplitudes required

for calculation of air velocity fluctuation magnitudes.

4.2 Bacteriological Methods

 

The test organism used in this investigation was

Serratia marcescens, which was selected on the basis of

 

its natural occurrence, nonpathogenicity, simple nutri-

tive requirements, production of a typical red colony,

 

59

 

Figure 4.11.—-Hot wire anemometer and auxilary
equipment.

 

Figure 4.12.—-X—Y recorder.

60

and the knowledge of its die—away characteristics at various

temperatures and relative humidities (Kethley, et al., 1957).

4.2a Handling Techniques

 

Each week, new transfers of the test culture were
started from the slant stock culture. The stock cultures
were maintained in tryptone-glucose—extract (TGE) agar
slant tubes, which were renewed at four to five week
intervals to ensure that the culture was stable. The
primary concern was to maintain the same variant of

Serratia marcescens, since previous work by Kethley, et a1.

 

(1956) had indicated a loss in stability with formation of
four variants with colonies of different colors. By
maintaining and starting new stock cultures at the
indicated intervals, the problem was kept to a minimum.
From the stock cultures, stored at 400 F., new
transfers were started weekly into 60 ml. 0.3% beef
extract broth and incubated at 32° C. Serial transfers
were made into the same broth at 48 hr intervals. The
broth culture was then used in an experiment after no

less than three serial transfers.

4.2b Plating and Counting

 

The agar media used as a collection surface in the
Casella slit air sampler was buffered, sodium chloride,
TGE agar. This medium which consisted of 24 g TGE agar,

five g sodium chloride, 2.5 g anhydrous dibasic sodium

61

phosphate and 1000 ml water was proposed by Kethley, et a1.
(1956) in order to reduce incubation time. Colonies were
counted with a Quebec counter after incubation of about

24 hr at 32°C.

4.3 Scope of Tests

 

The primary objective of the experiment was to
determine all required values needed to complete the
correlation of dimensionless groups presented in equation
3.42. In this relationship, the turbulent transfer
coefficient (kc) and eddy diffusivity (Dt) were of
primary importance and were evaluated for various inde-

pendent variables.

4.3a Turbulent Transfer Coefficient

 

The turbulent transfer coefficients (kC) were
evaluated according to equation 3.30. Values were
obtained at various conditions in each of the following
cases:

Opening size.—-The Opening between the two compart—

 

ments of the aerosol chamber had a set width of two feet.
However, turbulent transfer coefficients were determined
at vertical heights (H) of three, six and nine in.

Air flow.——The air flow settings selected were done
primarily on the basis of typical ventilation system
values for number of air changes per hour. Turbulent

transfer coefficients were determined for equal air flow

62

through each compartment of the aerosol chamber for a range
from 20 to 61 ft3/min. These represent a range of approxi—
mately 20 to 60 air changes per hr.

Air flow difference.-—Turbulent transfer coefficients

 

were determined for various settings in order to evaluate
the influence of an air flow rate difference between the
two compartments of the aerosol chamber. Values were ob-
tained at air flow rate difference intervals of ten ft3 per
minute up to a total difference of 40 ft3 per min. Deter-
minations were conducted with the flow rate difference in
the same direction as the concentration gradient and also

in the direction opposite the concentration gradient.

Geometry at initial mixing point.--The influence of

 

geometry of the point where the two air streams in the two
compartments join on the turbulent transfer coefficient

was determined by varying the thickness of the partition
between the two compartments. Experimental values were
obtained for partition thicknesses of 0.0625, 0.3125, 0.5525
and 4.5 in.

Temperature gradient.——Turbulent transfer coefficients

 

were determined for temperature gradients in the direction
opposite the concentration gradient by heating the air in
the low concentration compartment. The influence of a tem-
perature gradient in the same direction as the concentration
gradient was determined by heating the air in the high

concentration compartment.

63

4.3b Edgy Diffusivities

 

Two approaches to determining eddy diffusivities
were used as prOposed in section 3.4. The values were
determined for the same variations in independent variables

as the turbulent transfer coefficient.

4.3c General Procedures

 

Evaluation of the turbulent transfer coefficient
involved the establishment of a steady—state transfer
through the opening between the two compartments. This
was established by allowing the high concentration compart-
ment to attain an equilibrium concentration (the concen-
tration of the aerosol leaving the compartment was constant
with time). Then by sampling the air at the outlet of the
high and low concentration compartments, a steady—state
flux of aerosol through the opening could be calculated.
The calculation of the turbulent exchange coefficient
followed based on the Opening size and concentration
gradient.

The losses of aerosol due to death, gravity, deposits,
and transfer were calculated based on differences in con—
centration at the inlet and outlet of the high concentra-
tion compartment.

The determination of eddy diffusivities by the concen-
tration profile through the opening involved the collection

of air samples at 0.5 or 1 in.intervals across the Opening.

64

Since values produced rather large fluctuations, several
trials were involved in the establishment of a single
diffusivity.

The measure of turbulence or velocity fluctuations
with a hot wire anomometer (Flow Corp., 1958) to establish
an eddy diffusivity involved the recording of the velocity
fluctuation. This allowed establishment of a profile of
the intensity of turbulence through the opening for
various conditions. In addition, the calculation of the

eddy diffusivity from the equation 3.22 was possible.

4.4 Analysis of Turbulence Data

 

The recording of instantaneous velocity fluctuations
was used to determine the turbulent energy factor (ET?)
and autocorrelation coefficient (R(£)) as outlined in
section 3.2. The information obtained from each record
was in terms of voltage which represented an air velocity:

u = fi'+ u' (4.1)

A computer program to provide the desired information
was developed.

Since:

{IT—2'-

ZIP

z u'2 (4.2)

then:

u2 = (E + u')2 = u + 25 u' + u'2 (4.3)

 

 

 

2 u2 = XE? + E u'2 (4.4)
since:

211': 0 (4.5)
The turbulent energy factor would be defined as:

W=Z§zu2 -%252 (4.6)
and:

Zu = 2E = E (4.7)
so:

an“: E?- 52 (4.8)
Equation 4.8 was programmed to provide the calculation
of the turbulent energy factor (37?). Values are
presented in Table A-l4.

The autocorrelation coefficient was defined in
section 3.2 as:

R (a) = ”'(t) ”'(t + 5) (14.9)

377

In terms of equation (4.9), the product:

U'(t) U’(t + a) = [U(t) — 3] [m’t + a) —- u] (4.10)
Then, the autocorrelation coefficient becomes:
R(€)=u<t)u(t+g)-ma=ma+az (Ml)

 

377
Equation 4.11 was programmed to calculate the autocorrela—
tion coefficients presented in this investigation. The
programs were calculated by the Michigan State University

Control Data 3600 digital computer.

66

Analysis of data which required curve fitting was
conducted by using a library program E2 UTEX LSCFWOP
which approximated experimental data using the least

squares method.

5. RESULTS AND DISCUSSION

5.1 Characteristics of the
Aerosol Chamber

 

 

Preliminary tests were conducted to insure satis—
factory operation of the aerosol chamber. This objective
was attained by comparing performance of the chamber with

a standard ventilation equation:

C = C0 exp <- EVE) (2.6)

This equation has been used by Kethley, g§_§l, (1957) to
represent the dynamic emptying characteristics of an
aerosol chamber and the establishment of equilibration
times. The characteristics of one compartment of the
chamber used in this investigation are illustrated in
Figure 5.1. The data are somewhat scattered, but con-
firm the predicted expression. The standard errOr of
estimate (SEX) for agreement with-the predicted line was
$0.831 min. The data are most widely dispersed when the
chamber was nearly "empty" and approaching very low
counts. Due to this fact, small variations in counts
resulted in large variations in data presented.
According to Kethley, g£_gl. (1957), verification

of this equation indicates that the chamber is operating

67

68

 

 

\
\\ TestNo
0! I?
A \ v2 .8
50 3 \ Z: :I’O
r{ \\ xs 'vn
_\\ g \_ as can
\, \
\ .\
.. \ \
\ \
\ \
\ \
\ ‘ \
..\° \\ \
._- 8
\ \
E ‘4“ \
_|°P" 6‘ \
§ - 3\ v \
5." - 2 \
. \ \
F's \ . \
" \ - \
m 5— \ 9 \
\ ‘3 \o
- \\x \\
- .\ V\
\ a \ ..
u \~ 3 \~ 0
\ .. \
" \ \ A
\ I
\ \2
\ \
l 1 1 1 l 1 4__1
|o I 2 3 4 s s
fime,mm

Figure 5.1.--Dynamic emptying characteristics of aerosol chamber.

69

effectively with bacterial aerosols. However, the physical
meaning of the equilibration time requires further explan-
ation. For the chamber in this investigation, the concen-
tration of bacterial aerosol was increased to 99% Or reduced
to 1% (Figure 5.1) in 6 min. This equilibration time is
generally accepted in aerosol liturature as the duration of
time the aerosol is exposed to conditions in the chamber.
For example, Kethley, gt_gl. (1957) used this value as the
time factor for calculation of death rate constants for
air-borne bacteria. The validity of this usage may be some-
what questionable since not all of the aerosol particles

may be eXposed for exactly the equilibration time. The
design of the chamber requires that sufficient turbulence

be provided to maintain a uniform aerosol concentration.
Therefore, the possibility of all particles passing through
the chamber in the time indicated is questionable. Death
rate constants based on this time factor must be recognized
as average constants and their validity will depend on the
uniformity of the aerosol with respect to particle size and
characteristics.

In an attempt to obtain additional information on the
characteristics of the chamber, air flow measurements were
conducted at points throughout the chamber and primarily in
the vicinity of the opening between the two compartments of
the chamber. The first results of these measurements
revealed that it was impossible to accurately measure a

mean velocity with the hot wire anemometer. The reasons

70

were two—fold: (a) mean velocities in the chamber were
extremely low due to flow rates being used and (b)
turbulent fluctuations of the veloCity were very large
cOmpared to the eXpected mean velocity component. No
further attempts to measure mean velocity were made and
values used in calculations are based on the flow rate
through the chamber and the cross—sectional area of the
chamber. Mean velocities at each flow rate are presented
in Appendix Table.A—1. In addition, theoretical mean
velocity profiles based on equation 3.9 are presented for
conditions with different air flows through the two
compartments.

Since turbulence was found to be a significant
characteristic of the chamber, measurements to determine
the turbulent motion were conducted. Using a hot wire
anemometer and procedures described in section 4.4,
several values describing the turbulence were obtained.
From the variance of the instantaneous velocity fluctua—
tions, it was possible to determine the turbulent energy
«’57?

U

factor (u‘z) and the intensity of turbulence

The variation of both of these parameters are plotted
versus flow rate in Figure 5.2. Since the measurements
were obtained where y = o and x = 9 in, it is evident
that the intensity of turbulence, at this point, was not

significantly affected by flow rate. However, the results

r23

60" "2.4

(%)
8
l

r- 1.6

vs?
7?

E

sl sle‘u]

b|.2

20-0-03

'0!

 

Figure 5.2.—-Variation of

71

 

1 l 1 l I 1 L

20 30 40 50

"I
Air Flow Rate, 1., /min

turbulent energy and intensity of

 

 

 

 

 

 

 

turbulence with air flow rate.
w— ,
Flow Rom, "/min
0 -2I.3
_ A-ao
u - 40
v - 50
o - 6|
‘0—
g N
Elaw— —— : \ A
.. o
o
20—
p
c l l I i l l l l 44'
o 2 4 6 8

Transverse Distance, y, in

Figure 5.3.--Inf1uence of transverse location on intensity of
turbulence.

72

reveal that the turbulent energy factor increased steadily
for the range of flow rates measured.

The influence of location on the intensity of turbu-
lence is illustrated in Figure 5.3. The most Obvious
effect occurred with conditions of 21.3 ft3/min of air
through both compartments, where intensity of turbulence
decreased rapidly with distance from the partition. This H
particular result clearly indicated a "wake effect"
occurring due to the mixing of the two air streams at the
opening. The influence of this factor becomes less
evident when considering higher air flow rates. At flow
rates of 30 and 40 ft3/min, there was a significant
decrease at a distance of 8 in. from the Opening, while
at flow rates of 50 and 61 ft3/min, only slight decreases
could be detected. The most logical explanation of these
results is that the turbulence created by the diffusers
in each of the compartments becomes greater with increasing
flow rate. Apparently, air moving through the diffuser
at around 20 to 25 ft3/min remains in nearly laminar
streams until mixing occurs at the opening. At the higher
flow rates, the intensity of turbulence is higher through—
out the chamber and the influence of the wake is not
significant.

When an air flow gradient existed across the Opening,
the intensity of turbulence decreased in a rather uniform

manner from the high flow rate to the low flow rate side.

73

In general, the partition width and opening height had no

significant influence on intensity of turbulence.

5.2 Turbulent Diffusion
In order to describe the turbulent dispersion of an
aerosol by the fundamental equation 3.20, two parameters
are required: (a) the turbulent energy factor, and (b)

the autocorrelation coefficient, R(g).

5.2a Turbulent Energy

 

Although results presented in Figure 5.3 indicated
that location did not influence the intensity of turbu-
lence except at low flow rates, it is evident from Figure
5.4 that the influence of distance from the partition on
the turbulent energy factor may be significant even at
a flow rate of 50 ft3/min. The change in the turbulent
energy factor appears to be significant at all flow rates
except 61 ft3/min. However, the turbulent energy gradient
probably does not contribute significantly to dispersion
when compared to the turbulence mechanism and it may not
be necessary to consider this except at the low flow rate
(21.3 ft3/min) where the gradient is very critical.

At a flow rate of 21.3 ft3/min, the variation in the

turbulent energy factor can be described by the equation:

 

 

u'2 - ufiz u;
= erfc % JX (5.1)
ET? _ ET? vt

H L

74

 

  
 
 
    
   

1%
20' -*%—' V ——o———
|.8 '- Flow Rate, fl’/min
O - 6|
|.6 - A — 50
la - 40
L4 *- V - 30
x - 2|.3
l.2 -
$10-
03 -
.1
0.4 F
0.2 -
c l l 1 l L I I l I

 

 

-e -6 -4 -2 o 2 4
Transverse Distance, y, in

Figure 5.4.--Variation Of turbulent energy in transverse
direction.

0.99[
0.98

 

 

O
= o
écmw—
3
arm
5
0%
E as
:a
e 07
a .
ad
05

 

Figure 5.5.-—Agreement of experimental data with equation 3.16.

75

which is the wake solution to equation 3.2. This equation
should be very useful when describing transport at low
air flow rates.

The change in the turbulent energy factor (ET?) across
the mixing region between two different flow rates will
be described by equation 3.16. This equation can be used
to predict an apparent turbulent viscosity (vt) which is
constant across the mixing region. The agreement of
experimental data for the 50—20 air flow condition is
illustrated in Figure 5.5. Since the results are presented
on arithmetic probability coordinates, equation 3.16 is
represented by the straight solid line shown. The agree—
ment appears to be satisfactory for the limited data
presented and produces a standard error of estimate(SEy) Of
i0.02424 for the turbulent energy ratio.

Using equation 3.16 and turbulent energy factor
measurements obtained'at the opening, turbulent energy
profiles for various flow conditions are presented in
Figures 5.6, 5.7 and 5.8. The three conditions illustrated

3

in Figure 5.10 are for a flow rate of 70 ft /min on one

side of the partition. As is evident, the turbulent

energy profiles shift significantly to the low flow rate

3

side as that flow rate is decreased from 50 to 30 ft /min.

3

Similar profiles for flow rates of 60 and 50 ft /min on
the high flow rate side of the partition are presented in

Figures 5.7 and 5.8, respectively. In all cases, the

 
   
  
 

10" ~
‘~
b ‘\‘\\
“F‘ \ \\ Air flow condition = 70-30
\ in. .
__ \ s! 7;: 28 Irma
; ‘ Air tion condition =70-40 \\
x:mmw%M' \

  

 

 

Ml- / \
r Air tloa condition. 1 70-50 \. \\\
in
up ‘xsssos linin \\
i- \\
\
l 1 L 1 l 1 l L l 1 L 1 I L l 1 l 1 l 1 l _1_ 1
~10 -a -o -4 -2 o z 4 o a lo 12

Tranmm Distance, y, in.

Figure 5.6.——Turbulent energy profiles with 70 ft3/min. on
high air flow rate side.

  
 
    

‘\
\ \\Air tion condition =GO-30

'6’ 7; = 20.64”'/rnin
Air "on condition=GO-20 \\

“HOS"WMH \

* Air tion condition=60~40
o, .. X: 51.3""lmin

  

Hula-t Em” Ratio
2
ET

 

L 1 L _1 l 1 l J l 1 l 1 l 1 L 1 L 1 L 1 l _1_ I
4 -6 -4 -2 0 2 4 6 I IO 12 14

Transvom distance, y, in

Figure 5.7.-—Turbulent energy profiles with 60 ft3/min on
high air flow rate side.

 
   

\
\\ Air flow condition = 50-30

\ g "I.
Air "0' ( 7" 328| /min
condition=50-20\

  

0.0r"'\
“\\‘ AuMIwmmmwMi
‘ 7’ = I6.96""/rnin
«i- \

§

Air tlou condition 8 50y\‘\

a 7:145.” ""/inin

  
 

 

Tabled Energy Ratio

A l 1 I 1 l 1 L 1 I 1 l 1 l 1 l 1 L 1 1 1 I 1 I
" ~10 -a 4 -4 -z o 2 4 s a
Tronmm Distance, y, in

Figure 5.8.-—Turbulent energy profiles with 50 ft3/min. on
high air flow rate side.

77

profile representing the minimum difference in flow rate
is shifted toward the high flow rate side. One point of
interest is that profiles shifted to the right have a
common condition of 30 ft3/min on the low flow rate side,
while profiles from flow conditions with 20 or 10 ft3/min
are shifted to more central locations. An explanation

of these results (Figures 5.6, 5.7 and 5.8) is not readily
apparent. «However, by reference to Figures 5.3 and 5.4,
two factors were revealed: (a) the intensity of turbulence
for 21.3 ft3/min air flow at locations greater than 4 in.
from the Opening was very low (~5%) compared to values

3/min and (b) the turbulent

for an air flow of 30 ft
energy factor (J77) for a flow rate of 21.3 ft3/min
approached zero at locations greater than 4 in. from the
opening while the same value for 30 ft3/min was signifi—
cantly high even at 8 in. from the opening. The preceding
observations indicate that two different types of mixing

3

occur when the low air flow is 30 ft /min as compared to
21.3 ft3/min. In the first case, both air flows are
turbulent and contribute to turbulence in the mixing
region. The gradual shift of the profiles to the right
as the air flow difference increased exhibits an increase
in momentum transfer as would be eXpected. In the second
case, the mixing occurs between a turbulent air flow and

a laminar air flow resulting in less turbulence in the

mixing region. Although the momentum transfer may occur

78

to even greater extent, it is not indicated by the profiles

which illustrate turbulent energy (u'z) only.

5.2b Autocorrelation Coefficients

 

The second requirement for determination of disper-
sion of aerosol by turbulent diffusion is the autocorre-
lation coefficient R(€) defined in equation 3.21. Using
instantaneous velocity measurements obtained by procedures
outlined in section 4.4 autocorrelation coefficients were
calculated for 60 time lags (g) of 0.025 sec. Details
on the computer program and procedures used are presented
in section 4.4. A typical correlation curve for air flow
in the experimental chamber is shown in Figure 5.9. The
correlation curve decreases rapidly to negative values
before damping to zero, as expected based on previous
reports (Taylor, 1921; Frenkiel, 1953.) Data of this
type were obtained at several locations and air flow
conditions and all correlation curves were of the same
general type. Some problems were encountered with com-
plete damping to zero in many cases. This was attributed
to the lag time becoming large compared to the overall
sampling period. The influence of this factor on calcula—
tions to be presented is to produce values of somewhat
larger magnitude. Both the dispersion factor (y?) and the
eddy diffusivity (Dt) depend on the area under the corre-

lation curve and lack of damping would cause this value to

muo- Coefficient, a (£1

1‘3

0

. o

79

T

 

 

 

Figure 5.9.--Autocorrelation coefficients as influenced by

 
    
      
  

time lag.
0
li—
it
:1- '-,\
'2"
. -\

i\\
\

\i

I
a
a
O
a
o
a
I
u
a
o
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I
I
. t
v
a
I
o
I
I
O
o
O
O
O
O
a

F

E\\
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i

i
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www.m-

7

fl, on n.- mud/.111
so

---- w

 

—-—’°

aaaaaaaaaaa :‘3
.

\
i
\
i
\
\
1

 

l
2

i i
O I
Transverse Diatonco, in

J
3

Figure 5.10.——Variations in apparent mixing region width with

air flow and partition height.

80

 

 

 

 

 

 

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81

 

 

 

 

 

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82

 

 

 

 

 

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83

 

 

 

 

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84

be somewhat high. However, it is assumed that the area
produced by lack of damping is small and, in addition,
would be relatively consistent in all calculations.

The use of equations 3.25:

T t
377 = 2 F? / / 11(5) d5 dt (3.25)
O O

b — (Ff/2 - [2(Wfii-tlg (3°36)

with VT? replaced by ET? (assumption e. in section 3),
allows calculation of the statistical dispersion and an
apparent mixing region width (b). As is evident from
equation 3.36, the mixing region width is directly depen-
dent on the dispersion time (t). The selection of a

proper dispersion time for the aerosol moving from the high
to the low concentration compartment of the aerosol chamber
was not easy. The most likely selection appeared to be the
equilibrium time discussed earlier in section 5.1. Since the
dispersion did not start until the aerosol and filtered air
came in contact at the initial point of mixing, aerosol moving
from one side to the other was not exposed for the entire
equilibration time. Calculations are based on dispersion
times which are a fraction of the equilibration time. The
fraction is based on the location of the initial point

of mixing with respect to the overall height of the

aerosol chamber. Using dispersion times (t) and equation

85

3.36, the apparent mixing region widths in Table 5.1 were
calculated. The influence of air flow rate on the apparent
mixing region width is illustrated in Figure 5.10. The
results indicate that the width (b) increases with increas-
ing flow rate. This relationship exists even though the
dispersion time (t) increases significantly with decreasing
flow rate.

In addition to statistical dispersion and apparent
mixing region width, the autocorrelation coefficient is
required in the calculation of the specific eddy diffusi—

vity (Dt) according to equation 3.32:

t
D1: = 1770/ R(€) d: (3.32)

These values have been calculated for the required air

flow situations and are presented in Table 5.1.

5.3 Concentration Distributions

 

In order to verify equation 3.17, which indicates
that the concentration distribution in the mixing region
should be described by some form of the error function,
point concentration measurements were conducted in a
limited number of situations. Measurements Obtained
permitted calculation of a single eddy diffusivity value
at each point in the concentration profile. The values
varied considerably; however, in order to satisfy equation

3.17, the apparent eddy diffusivity (Da) must be constant.

A mean of the values obtained in the concentration profile

86

was used to present the data in Figure 5.11. Data obtained
with flow conditions of 50 ft3/min in the high concentra-
tion compartment and 50 ft3/min and 30 ft3/min in the low
concentration compartment give good agreement with the
proposed function.

The obvious weakness to the above method for deter-
mining eddy diffusivity values is lack of experimental
accuracy for obtaining point concentration data. In
addition, the function requires that the eddy diffusivity
be constant in the mixing region which may or may not be
true: Use of equation 3.22 allows calculation of specific
eddy diffusivities (Dt) at points in the profile. There—
fore, the values obtained by point concentration measure-
'ments will be referred to as apparent eddy diffusivities

ma).

5.4 Transport of the Bacterial Aerosol

 

The complete description of the transport of a
bacterial aerosol will combine two phases of study: (a)
experimental determination of turbulent transfer coeffi—
cients (kc) defined by equation 3.30 and (b) use of the
dimensionless transport relationship presented in equation

3.42,

5.4a Experimental Transfer Coefficients

 

The influence of air flow rate on the experimental

turbulent transfer coefficients (kc) is illustrated in

Elia

‘1

87

.Cowmoa mCHxHE CH soapsofihpmfip COHpmapcoocOOIl.HH.m masmflm

E .H .8555 3858:.

 

 

 

 

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8.8-6 3 tel 15..
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552.8 .2... .2
a c

 

01103 uoiiaiiuaouog

88

Figure 5.12. The experimental data produced a coefficient
of variation of i0.l76 for kC from the curve selected
according to procedures presented in section 4.4. As is
evident, the coefficient (kc) increases significantly
between 20 and 40 ft3/min, but becomes relatively constant
above 40 ft3/min.

Results (Figure 5.13) reveal the influence of air
flow rate gradients on the turbulent transfer coefficient.
For aerosol flow rates of 40 and 50 ft3/min, the coeffic—
ient was maximum at equal flow rates. If the aerosol
flow rate was 30 ft3/min, the maximum transfer coefficient
occurred between air flow gradients of -15 and —20 ft3/min.

Figure 5.14 presents the relationship between a
temperature gradient across the mixing region and the
transfer coefficient (kc). The correlation appears to
be linear for the range of gradients investigated with a
standard error of estimate (SEy) of :(0.651 for experimental
coefficients. The best fit curve for the experimental
points can be described by the following equation:

kc = 0.2195 119 + 5.09 (5.2)

Since the influence of a temperature gradient on
transport of the bacterial aerosol in the mixing region
could be related to several factors, an attempt was
made to isolate a portion of the influence. Several
investigators (Kethley, gt_al,, 1956; DeOme, gt_§l., 1944;

Webb, 1959; Hayakaw and Poon, 1965) have determined and

1.1

89

l

Turbulent Transfer Coefficient, kc
b
l

 

, 1 1 1 1 1
I0 20 so , 40 so
Air Flow Rate, f., f'/rnin

Figure 5.12.-~Variation of transfer coefficient with air flow
rate.

\

Turbulent Transfer Coefficient, ltc

   

'1’

Aerosol Fla-l rate ft‘/min.
30 -—-——
4O —— \
P so -----

0 J l I l l l l l J
-40 -20 o , 20 40
Air Flori Rate Difference, Af, n/min

 

Figure 5.13.--Influence of air flow rate gradient on transfer
coefficient.

 

60

i-

L—o .

 

9O

discussed the influence of temperature and relative

humidity on viability of bacterial aerosols. Since the

temperature gradients maintained in the aerosol chamber

were developed by heating the air, both factors could

contribute to the relationship illustrated in Figure 5.14
Death rate constants for aerosols of Serratia

marcescens were determined by Kethley, et a1. (1956)

 

for various temperatures and relative humidities. These
data indicate the drastic influence of relative humidity
along with the influence of temperature. However, experi—
mental data were available only up to 80°F. while data

of this investigation were obtained at temperatures as
high as 98.5°F., therefore, extrapolation was required.
In order to extrapolate the available death rate informa-
tion as accurately as possible, the data were presented
on semi-logrithmic coordinates as shown in Figure 5.15.
Use of the loglccversus 1/6a relationship implies that
the death of air-borne bacteria obeys a first-order
kinetics reaction. This type of relationship has been
used successfully by Webb (1959) and Hayakaw and Poon
(1965). Results in Figure 5.15 indicate two stages of
death, at least at lower relative humidities. The
influence of temperature on death rate is small from 40°
to about 70°F., but becomes very significant as the

temperature increases above this level. The death rate

Turbulent Transfer Cull-dent, t.

 

Figure 5.14.—-Inf1uence

IIYVII]

I /..

“I
I

M! Role Constant,

 

91

    

1,- aizsmov 5.0910615

Steward Error of [oi-note t 20015 for I,

l L
.14 -m -s -2 o 2 6 to lo
Ten-perature Grad-ant. be."

of temperature gradient on transfer
coefficient. -

 

Relative Nullllly,°/9
0 - 00
A - 70
D - 60
V -50
1 -4o

.1 l 1 l 1 l l l
19’) 19 I65 18

inverse Aowiule Temperature, I/9.°R

Figure 5.15.--Influence of temperature and relative humidity
on death rate of Serratia marcescens»

Turbulent Transfer Coefficient, I,

 

 

 

[I'fliOIBfol

-—— Account-M lav «Iii-tr chance

I l l 1 I 1 1 1 l 1
44 -IO ~‘ '2 3 2
annual-in Gradient, 119. °F

1 l L 41__j
‘ lo I.

Figure 5.16.——Influence of aerosol viability on the relation-
ship between temperature gradient and transfer coefficient.

.4“

constants used to account for viability changes due to
the temperature gradient were obtained from Figure 5.15.
By adjusting the experimental turbulent transport
coefficients to account for changes in viability during
transport, the data illustrated in Figure 5.16 were
obtained. The results reveal an increase in the coeffic—
ients (kc) at negative temperature gradients and a
decrease at positive temperature gradients. However, it
is evident that viability does not account for the entire
influence of the temperature gradient and other factors

must be contributing to the apparent transport.

5.4b Dimensionless Relationships

 

In order to describe the transport of bacterial
aerosols due to turbulent diffusion, dimensionless trans—
port groups derived in section 3.5 will be used. The
influence of each of the five basic parameters will be
presented and-discussed separately and then all data
except that obtained for a temperature gradient will be
used to establish an eXpression to describe the influence
of all parameters.

The influence of dispersion time (t) and mean air

ke Dt / f(B)

velocity (u) on dimensionless transport
u'zb bo
O
is illustrated in Figure 5.17. The results indicate an

increase in transport with an increase in the dimension-

less value (£,/Et) and reveals that the influence of the

93

.zpfiooao> saw some cam
oEHp coampoamfie Noocoasnpzp mp econo3Hmcfl mm pLOOmcmLp mmOHCOHmcoEHQII.OH.m oaswflm

 

     
  

 

E
Oo_ x 4%-
OO ON OO OO OO OH ON 2 OO
_ H _ _ _ H _ _
\ 1 _ O
\\
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58.23252 3 as... 2225 1 .
ONOOO e \\ NO
ONsO .N. \ m \
ONOO.O - o \ \ \
:5 52; see: \ IHO
\
\
\
lie
T5588 - .5 we
.N «D 01
13
1 NO
\ .
\ 1 OO
\
\
\
\

 

ssaiuoisuauiig

lJOdSUDll

°q all 1
10 9)‘

 

J.
/

°q

(€11

94

length scale of turbulence (2,) dispersion time (t) over-
shadows that of the mean velocity (3). The relationship
is approximated very well by the equation:

kCDt = 0.00796 fl 5451 — 0.0139

ETTbO at bo
for the three partition widths at the initial point of
mixing. The standard error of estimate (SEy) is t0.0868
for the dimensionless transport group.

The influence of gradients in air flow between the

two compartments of the aerosol chamber on the dimenSion—

k D
less transport group —9——3 is presented in Figures 5.18,

ET7bO
5.19 and 5.20. For all three situations (50, 40 and 30
ft3/min through the high concentration compartment), the
transport decreases with an increasing positive air flow
gradient. However, the influence of a negative gradient
is not consistent. For f0 = 50 ft3/min (Figure 5.18),
the transport decreases with increasing negative air
flow gradient in about the same manner as indicated for,
a positive gradient. The transport also decreases for
small negative air flow gradients with f0 = 40 ft3/min
(Figure 5.19), but becomes relatively constant at a
higher level than the positive gradient. When fO was
decreased to 30 ft3/min, the transport increased with

increasing negative air flow gradient before decreasing

to a level nearly equal to that at equal air flow rates.

95

The transport characteristics illustrated in Figure 5.18,
5.19 and 5.20 are probably more closely related to turbu-
lence in the mixing region than to the mangitude of the

air flow gradient. This is clearly evident from Figure 5.20
where the dimensionless transport was low with equal

flow rates of 30 ft3/min. By increasing the flow in the
low concentration compartment, the turbulence and transport
‘both increased. This corresponding increase in both para-
meters continued until momentum transport from the low to
the high concentration compartment was sufficient to over-
come the increased transport due to turbulence. This

same sequence of events did not occur at high air flow
rates since turbulence levels were sufficiently high to
produce nearly maximum transfer at equal flow rates. An
increase in negative gradient did not increase turbulence
enough to overcome the influence of increased momentum
transfer. The increase in positive air flow gradient

does not reflect an apparent influence of momentum trans-
fer, indicating that the decreases resulted in signifi—
cant decreases in turbulence.

Results (Figure 5.21) reveal the influence of parti-
tion width and apparent mixing region width on the dimen-
sionless transport group. Several factors are illustrated
by the results, however, most evident is the increase in
transport with increasing partition width followed by a

decrease to a level nearly equal to the transport with

 

96

071—

ad

- \ Au no. Rm = sori’j-u-r-

 

Pas-tive Gradient
0.5 - \ — — — Newt-n Grad-ant

g 0.4 1—
g
.z
.2 0.3 '—
5 0.2 -

0|—

 

 

C)

0 0.! 0.2 0,3 0 4 0.5 06 0.7 0.8
111
la
Figure 5.18.-—Variation in dimensionless transport with air
flow rate gradient for aerosol flow rate of 50 ft3/min.

 

as s
1,: 101- /---i--

_— Positive Gradient

— —- Negative Gradient
0 5

5|;
.1 I!

 

 

 

. l l l l l l l J

0 0| 02 0.3 0,4 0 5 0 6 0.7 0.8

.NIE

Figure 5.19.—-Variation in dimensionless transport with air
flow rate gradient for aerosol flow rate of 40 ft3/min.

 

 

 

7 r—-
P
61—
,. Air ria- Rate of 3011’In-n
liar-um Grad-em
‘5 3 5._ ———-Neqot-: Gradient
:15.-
- 1- /’—‘\\
'5 a / \
e , \
r- / \
v- / \
E 3_ / . \
.§ // \
C
c 7 \.
6 I
Z '- \
I h—
. 1 L 1 l 1 l 1 l 1 l 1 1 JJ
"0 02 or as as 10 12 14
09/“

Figure 5.20.—~Variation in dimensionless transport with air
flow rate gradient for aerosol flow rate of 30 ft3/min.

97

the narrow partition. The increase detected must be due
to increased turbulence in the mixing region even though
it was not detected by measurements. It seems possible
that small increases in turbulence could occur in the,
mixing region without detection and cause increased
transport. The decreased transport with an even wider
partition would be due to a significant decrease in the
apparent mixing region width while turbulence may have
increased only slightly.

The relationship between the dimensionless transport

3:2:
group £77 b and dimensionless opening height (H/H')
o

is presented in Figure 5.22. The decrease in transport
per unit area with increasing opening height is apparent
in all flow situations, but is most significant at equal
flow rates. An explanation of this relationship is
probably related to results presented in Figure 5.10 where
the apparent mixing region width was shown to be a
function of the square root of the distance from the
initial point of mixing. Therefore, transport per unit
area based on the dispersion-entrainment mechanism would
larger for small Openings.

The relationship between the dimensionless transport
kc Dt
group ETYb and dimensionless temperature (eHC/GLC) based
O

 

on the temperature gradient is presented in Figure 5.23

98

08r-

1W)

..0
o
I

/

k0-

D-n-ens-onless Transport, “5.5.
O O
a U!
T I

o
1.,-
l

o
N
l

Oli-

 

  

1-1 $11- 11%.-
0 -50
A -40
-30

Figure 5.21.-—Inf1uence of partition width on dimensionless

transport.

 

 

 

IZ—
D
S IO— Air Flo- Rate D-ffcuncollt'lmn)
:lA 1- 0 ‘0
\ A -lO
0- 3 .p— U ‘20
.218 v -2er
_ . X -393
5
o. 1‘
ts— '
..:
§
" 41-
1;:
C
E 1-
5
2_ \
A 1 1 1 1 4m
" 005 01 one 0.2
H
lH'

Figure 5.22.-—Inf1uence of Opening height on dimensionless

‘cD'
16gb.

D-rnensionleu Transport

transport.

 

 

 

6!—
5r—
4»—
3.—
11, 0.
2L- 0 Standard Error of Est-note = 201501 for =———
11"!)°
l—
,__,1 l 1 4 1 1 l 1 1 1 1 I 1 L 1 1 1 1 1 1 1 J
o ' 03 09 10 11 1.2
0
“/01:

Figure 5.23.——Inf1uence of dimensionless temperature ratio
on dimensionless transport.

99

This relationship is very similar to the linear relationship

presented earlier in Figure 5.14

 

kc Dt
u' b = 16.29 (eHC/eLC )

O

— 12.1 (5.4)

where 6H0 and 6LC represent temperatures in the high and
low concentration compartments respectively. An adequate
explanation of the influence of temperature gradient
other than the influence on viability is not apparent. A
possible explanation is that convective heat transfer and a
vapor pressure gradient across the mixing region contri-
bute or decrease the transport of bacterial aerosol. The
influence of these two factors would be in addition to
the turbulent transport normally present.

The dimensionless transport equation derived in
section 3.5 was:

k D u v D
c t = K‘ f(B) L t _E (3.“2)

u'zbO b0 u'2 H vt

 

where K' represents a constant to be determined from
experimental data. Using all data obtained without a
temperature gradient, the slope of the straight line
approximated by the least squares method was 0.01276.
Therefore, K' = 0.01276 and equation 3.42 becomes:

kc D 0 D

U.
t = 0.01276 féB) —£——45 33
u'zbO o u'2 H t

+ 0.772 (5.5)

 

 

100

Additional investigation indicated that data obtained
with a temperature gradient could be described reasonably

well by the same relationship by using the temperature

ratio (GHC/BLC) as an exponent to the dimensionless trans—
uL Vt
port group ET? H . This provides the following dimen-

sionless relationship for data presented in Figure 5.24:

)Dt + 0.7u1

 

 

k D G' v (9 /0
c t = 0.0136“ f(8) L t HO LC

u'zbO b0 u‘2 H Vt

(5.6)

This relationship describes the transport of bacterial
aerosols for all parameters studied in this investigation.

The standard error of estimate (SEy)_Of'il.OOU for dimen—~

sionless transport values applied for a range of dimension—

less turbulence values from 0 to 0.7.

lOl

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6. SUMMARY AND CONCLUSIONS

1. By increasing the air flow rate gradient between
two turbulent air streams, an increase in momentum transfer
was indicated. A significant shift of the turbulent energy
profiles to the lower flow rate side was revealed for rates
of 30 ft3/min or higher. At flow rates of less than 30 ft3/

min on the low flow rate side, an apparent decrease in

momentum transfer resulted due to decreased turbulence in
the mixing region.

2. Concentration distributions in the mixing region
gave good agreement with the expression:

C — C‘ u

 

L l y L
1" = — l - erf
CH - 6L 2 2 Da x

where Da is an apparent eddy diffusivity which is constant
in the mixing region.

3. Transport of bacterial aerosol in a turbulent
mixing region increased with increasing equal flow rates.
The following relationship obtained from experimental data:

kc Dt = 0.00796 :l— f(8) - 0.0139

u'zbO ut bo

 

 

indicates that transport is a significant function of
turbulence and dispersion time and is only slightly
influenced by Changes in mean air velocity.

102

 

103

3/min, transport of

A. At air flow rates above 30 ft
bacterial aerosol was maximum at equal flow rates through
both compartments of the aerosol chamber. At these flow
rates, transport decreased with increasing positive or
negative air flow rate gradients.

5. The width of partition at the initial point of
mixing had only a slight influence on transport at air
flow rates of 30 ft3/min or higher. Transport increased
at a partition width of 0.3125 in., but decreased as the
width was increased to 0.5625 in. The decrease was
attributed to a decrease in mixing region width corres—
ponding to the increase in partition width.

6. Transport of bacterial aerosol decreased with
increasing Opening height. This was related directly to
the apparent mixing region width, which was a function of
the square root of the distance from the initial point of
mixing.

7. A temperature gradient across the mixing region
influenced transport of the bacterial aerosol as indicated
by the expression:

kc D

t
u'zb
o

 

= 16.29 (eHC/eLC) — 12.1

which applies to a range of temperature gradients from —lAO

to +12.5°F.

 

104

8. The tranSport of a bacterial aerosol was described
by the following dimenSionless relationship, which considers

all parameters studied:

*

 

k D , p u- v (6 /6 -) D
_E__£ = 0.01364 féB) _£__E_ HC LC —£- + 0.741
u'zbo o W}: “t

This relationship applies for dimensionless turbulence

valués between 0 and 0.7.

7. RECOMMENDATIONS FOR FUTURE WORK

The results of this investigation indicate the need

for additional work in the following areas:

1.

Investigation of turbulence levels and momentum
transfer in mixing regions between laminar and
turbulent air streams.

Additional investigation of transport mechanisms
present in mixing regions formed by an air flow
rate gradient.

Further investigation of mechanisms related to
transport of bacterial aerosol in mixing regions
as influenced by partition width at the initial
point of mixing.

Investigation of bacterial aerosol transport
with a temperature gradient across the mixing

region.

105

 

 

APPENDIX

106

APPENDIX

A.l Air Flow Measurement

 

From Eckman (1950), the following equation was
used to calculate air flows through both compartments of

the aerosol chamber:

 

2 2
n CVT B D ¢V

q = b /M'(\)m — v? 1 ————2gh
II /————¢1 _ 8 Mb V. /

 

 

 

where:
q = air flow rate, ft3/sec
CVT = venturi discharge coefficient
8 = diameter ratio = d/D
D = pipe diameter, ft.

9 = rational expansion ratio

vb = specific volume of gas at base conditions, ft3/lb.
Mb = moisture factor at base conditions

M, = moisture factor at upstream conditions

Vm = weight density of manometer fluid, lb./ft3

0 = density of fluid over manometer fluid, lb./ft3

f
g = acceleration due to gravity, ft/sec.2
h

= manometer differential, ft.

107

108

Table Arlshows the corresponding air flow rates and

pressure drOp values used in this investigation.

TABLE Aal——Pressure drop, air flow rate and mean air

velocity

 

 

 

 

 

Mean air _

Pressure Drop Air flow rate velocity (u)
(in. H20) (ftj/min) ‘(ft/min)
0.018 10.7 0.667
0.074 21.3 1.333
0.260 40 2.500
0.410 50 3.120
0.550 58 3.625
0.600 60 3.750
0.610 61 3.813
0.800 70 4.375

 

and

A.2 Solution to Diffusior Equation
According to equation (3.8):

_ . D 32
u 3? — a a 2

J

O

k

9::

boundary conditions (3.11), (3.12) and (3.14):

H
C)

At x n 0, y > 0: C L
X>O,y=oo: C=CT
“ C —C

H L
x > O, y = 0: C = CL + 2 -—

 

(A.

(.1
(A

l)

.2)

.3)
.4)

109

The solution to equation (A.l) will be of the form:

O: f (11‘, Da,

By use of linear relationships between variables, it is

 

evident that: ‘
_ E
C-AF y/Dax) (A.

 

 

 

 

By substitution of equation (A.6) into equation (A.l):
F'Kn) = - % F'(n) (A.
where:
_. Lil;
n - y D x (A.
['8'
By solving the differential equation (A.7):
n
PM) = c = A / epr-(n/2)1dn + B (A.
0
Since:
n
2 [ expE—nz] an . (A.
H? 0
is equal to the Gaussian error function, equation (A.9)
can be expressed as:
= 1 /J
C A erf <; D x + B (A.
a
Using the stated boundary conditions:
C —C C -C
- H L . _ H L
A — - 2 , 13- CL + 2 (A
So: _
C C _l
- L 1 y E
= — l — erf ——— (A.
CH-CL 2 2 Dax
L _.

 

 

X. y) (A.

5)

6)

7)

8)

9)

10)

11)

.12)

13)

110

.mHHmosQ mpfiooflo> Lam smozll.a.< opsmfim

E ;.. 13835 $13,?ch

 

 

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. 4. a _ _ _ 4 _ a M . M _ _ a _ o
mu
1L. MW
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WV.
1 M
w
EE\:_.m .11“
. n...
.52?2. $8 m/H.
:_E\n:m._~ u
11m

 

 

 

111

A.3 Mean Air Velocity Profile

 

Using the solution to the equation of motion as

presented in equation (3.15):

5|
l
c
l
NlI—J

 

lverf 521

 

VX

a predicted mean velocity profile can be obtained. The

profile for the air flow conditions of 50 ft3/min in one

3

compartment and 21.3 ft /min in the other compartment of

the aerosol chamber is present in Figure A.1.

A.4 Experimental Turbulent Transfer
Coefficients

 

 

The data presented in Tables A.2 through A.13
represent individual trials conducted to determine the
turbulent transfer coefficients (kc) for various situations.
From equation 3.30, it is evident that:

NA

kc = A(CHVCL (A.14)
In the following tables, the steady—state transfer
represents counts in air samples collected at the low con—
centration compartment outlet. The mass flux (NA) was
calculated from the mean of the steady—state values for

flow rate in the low concentration compartment. The turbu—

lent transfer coefficient was calculated from equation A.14.

112

TABLE A-2.-—Inf1uence of air flow rate on transport charac-

 

 

 

 

 

teristics of air-borne bacteria with 1.5 ft2 opening.
Air Flow Steady-State Mass Concentration Transfer

Rate Transfer Flux Gradient Coefficient
[No./min-ft2
(ft3/min.) (No./ft3) (No./min.) (No./ft3) (No./ft3)]

61 22-21-25 1382.66 189 4.8771

22-27-24 1484.33 170 5.8209

24-22-25 1443.66 154 6.2496

54-50—44 3009.33 405 4.9536

58 25-24—16 1256.67 157 5.3362

42—34—27 1991.33 250 5.3102

27—19-25 1372.66 221 4.1408

35-31-33 1914.00 269 4.7435

50 54-47-50 2516.66 375 4.4741

70-51-68 3150.00 387 5.4264

36—40-38 1900.00 216 5.8642

54-29-36 1983.00 238 5.5556

40 75-77—62 2853.33 358 5.3135

87-65-67 2920.00 342 5.6920

69-80-65 2853.33 415 4.5837

77-63-79 2920.00 396 4.9158

30 28-38-31 969.99 283 2.2850

37-37-26 999.99 242 2.7548

61—61—58 1800.00 375 3.2000

29—66-70 1650.00 382 2.8796

43-38—42 1230.00 332 2.4699

65-46-57 1680.00 373 3.0027

21.3 21—22—23 468.60 436 0.7165

17-34—21 511.20 441 0.7728

24-24—26 525.40 407 0.8606

21-28-29 553.80 400 0.9230

 

113

TABLE A-3.—-Inf1uence of air flow rate gradient ogutransport
characteristics of air—borne bacteria3with 1.5 ft opening
and aerosol flow rate of 30 ft /min.

 

 

 

 

 

 

 

Air Flow
Rate Steady—State Mass Concentration Transfer
Difference Transfer Flux Gradient Coefficient
3 3 3 [No./min-ft2
(ft /min) (No./ft ) (No./min) (No./ft ) (No./ft3)]
19.3 52-39-41 470.80 326 0.9628
37-40-55 470.80 382 0.8216
8.7 36-39-43 837.80 261 2.1399
40-40—43 873.30 308 1.8903
28-20—20 482.80 187 1.7212
—10 49-54-58 2146.67 284 5.0391
45-44—48 1826.67 220 5.5354
~20 57—46—62 2750.00 445 4.1199
72-75-46 3216.67 482 4.4491
32-27-34 1550.00 198 5.2189
25—28-51 1900.00 205 6.1789
—30 42-39-30 2120.00 295 4.9717
33-31—31 1900.00 277 4.5728
73-78—80 4620.00 484 6.3636
73-54-61 3759-99 432 5.8025
—40 40—38-26 2426.67 400 4.0444
28-29-35 2146.67 369 3.8783

 

114

 

 

 

 

 

 

TABLE A-4.-—Influence of air flow rate gradient 02 transport
characteristics of air-borne bacteria with 1.5 ft opening
and aerosol flow rate of 10 ft3/min.
Air Flow
Rate Steady-State Mass Concentration Transfer
Difference Transfer Flux Gradient Coefficient
3 3 3 [No./min-ft2
(ft .min.) (No./ft ) (No./min.) (No./ft ) (No./ft3)]
29.3 48—53 540.35 323 1.1153
63-64-65 684.80 307 1.4871
18.7 52-69-93 1519.40 357 2.837
60—67-92 1554.90 356 2.911
10 89-91—88 2680.00 352 5.0758
98—97-93 2880.00 431 4.4548
—10 38-37-35 1833.33 291 4.2001
33-25-34 1533-33 263 3-8868
24-30—27 1350.00 170 5.2941
23-48-24 1416.67 168 5.6217
-20 39—30-34 2060.00 306 4.4880
26—28—32 1720.00 262 4.3765
-30 40—39—37 2706.67 486 3.7129
35—36—32 2403.33 446 3.5924

 

115

TABLE A—5.-—Inf1uence of air flow rate gradient o5 transport

 

 

 

 

 

 

characteristics of air—borne bactegia with 1.5 ft opening
aerosol flow rate of 50 ft /min.
Air Flow
Rate Steady-State Mass Concentration Transfer
Difference Transfer Flux Gradient Coefficient
3 3 3 [No./min. ft2
(ft /m1n.) (No./ft ) (No./min.) (No./ft ) (No./ft3)]
39.3 35—35—42 399.47 398 0.6691
33-28-35 342.40 342 0.6675
26—27-29 292.47 186 1.0483
17-11—17 160.50 154 0.6948
28.7 38-39-43 852.00 255 2.2275
38—44—37 844.89 207 2.7211
92-60—53 1455.50 389 2.4944
42—34-45 859.10 300 1.9091
20 56-68-63 1869.90 425 2.9333
71-49-54 1740.00 403 2.8784
31—34—39 1040.00 225 3.0815
10 31—23—27 1080.00 187 3.8503
28—21—12 813.33 174 4.6743
15-38-33 1013.30 191 3.5369
-10 50—58-48 3120.00 366 5.6831
36-31—34 2020.00 303 4.4444
30-32-28 1800.00 272 4.4118
-20 44-33—32 2543 33 447 3.7932
29—29-34 2146.67 418 3.4237

 

116

TABLE A—6.——Influence of width at initial point of mixing
on transport characteristic§ of air-borne bacteria at
/

 

 

 

 

 

 

 

50 ft min.
Partition Steady-State Mass Concentration Transfer
Width Transfer Flux Gradient Coefficient
3 3 [No./min§ft2
(in.) (No./ft ) (No./min.) (No./ft ) (No./ft )1
0.3125 44—46-51 2350.00 272 5.7598
47-35-41 2050.00 264 5.1768
78-55—72 3415.67 321 7.0959
65—60—34 2650.00 291 6.0710
0.5625 24-27—33 1400.00 253 3.6891
33—26—38 1616.67 246 4.3812
25—32—32 1483.33 209 4.7315
40-27-36 1716.67 243 4.7097
29-23-42 1566.67 308 3.3911
43—52—47 2366.67 330 4.7811
4.5 53-59—51 2716.67 428 4.2316
40-35-42 1950.00 350 3.7143
0.0625 54—47-50 2516.67 375 4.4741
70-51-68 3150.00 387 5.4264
36-40-38 1900.00 216 5.8642
54—29—36 1983.00 238 5.5556

 

TABLE A-7.--Influence of width at initial point of mixing

117

on transport characteristics

of air-borne bacteria at

 

 

 

 

 

 

40 ft3/min.
Partition Steady-State Mass Concentration Transfer
Width Transfer Flux Gradient Coefficient
3 3 [No./min-ft2
(in.) (No./ft ) (No./min) (No./ft ) (No./ft3)]
0.0625 75-77-62 2853.33 358 5.3135
87-65-67 2920.00 342 5.6920
69-80-65 2853.33 415 4.5837
77-63-79 2920.00 396 4.9158
0.3125 57-40-42 1866.67 230 5.4106
71-60-57 2506.67 254 6.5792
0.5625 58-44-51 2040.00 297 4.5791
52-48—49 1986.67 284 4.6635
53-30-47 1733-33 310 3-7275
34-47-41 1626.67 305 3.5556
4.5 56-46-50 2026.67 297 4.5492
70-57-55 2426.67 322 5.0242
37-28-29 1253.33 267 3.1294
32-41—43 1546(67 249 4.1410

 

 

118

TABLE A-8.--Influence of width at initial point of mixing
on transport characteristicg of air—borne bacteria at

 

 

 

 

 

 

30 ft /min.
Partition Steady-State Mass Concentration Transfer
Width Transfer Flux Gradient Coefficient
3 3 [No./min—ft2
(in.) (No./ft ) (No./min.) (No./ft ) (No./ft3)]
0.0625 28-38—31 970.00 283 2.2850
37-37-26 1000.00 242 2.7548
61-61—58 1800.00 375 3.2000
29-66-70 1650.00 382 2.8796
43-38-42 1230.00 332 2.4699
65-46—57 1680.00 373 3.0027
0.3125 50-59-66 1750.00 293 3.9818
57-67-69 1930.00 310 4.1505
0.5625 46-44-38 1280.00 348 2.4521
61-58-67 1860.00 437 2.8375
50-39-36 1250.00 315 2.6455
27-36-49 1120.00 293 2.5484
4.5‘ 16-28-13 579.00 237 1.6287
19-17-44 800.00 218 2.4465
31-35-39 1050.00 323 2.1672
27—44-40 1110.00 363 2.0386

 

119

TABLE A-9.——Influence of air flow rate gradient on transport
characteristics of air-borne bacteria with 0.3125 in.

 

 

 

 

 

 

partition.
Air Flow

Rate Steady—State Mass Concentration Transfer
Difference Transfer Flux Gradient Coefficient
3 3 3 [No./min—ft2
(ft /min.) (No./ft ) (No./min.) (No./ft ) (No./ft3)1

“39.3 15-12-19 164.07 158 0.6923

11-9-10 107.00 134 0.5323

75-67-85 809.63 669 0.8068

56-48-42 520.73 551 0.6301

28.7 46-42—42 923.00 302 2.0375

38—38—37 802.30 229 2.3357

54—41—58 1086.30 415 1.7451

79-98-54 1640.01 425 2.5726

20 26-27-15 680.00 144 3.1482

25-38—33 960.00 204 3.1373

10 35-41—35 1560.00 197 5.2792

96-78-92 680.00 544 4.3464

101-117-116 3546.67 673 4.4114

0 44-46—51 2350.00 272 5.7598

47-35-41 2050.00 264 5.1768

78-55-72 3416-67 321 7-0959

65-60—34 2650.00 291 6.0710

—10 10-13-11 680.00 97 4.6735

 

120

TABLE A-10.--Inf1uence of air flow rate gradient on trans—
port characteristics of air—borne bacteria with 0.5625 in.

 

 

 

 

 

 

partition.
Air Flow
Rate Steady—State Mass Concentration Transfer
Difference Transfer Flux Gradient Coefficient
3 3 3 [No./min-—ft2
(ft /min.) (No./ft ) (No./min.) (No./ft ) (No./ft3)]
39.3 12—15—11 135.53 131 0.6897
10—13-8-16 125.73 155 0.5408
18—7-13 135.53 108 0.8366
13-12-16 146.23 119 0.8192
28.7 25—18-21 454.40 178 1.7019
21-26—20 475.70 187 1.6959
20 21-17-13 510.00 110 3.0909
16—15—8 390.00 88 2.9545
10 37—28—28 1240.00 216 3.8272
23-14-15 693-33 137 3-3739
23-16-16 733 33 153 3.1954
0 24—27-33 1400.00 253 3.6891
33-26—38 1616.67 246 4.3812
25—32—32 1483.33 209 4.7315
40-27—36 1716.67 243 4.7097
29-23-42 1566.67 308 3.3911
43—52-47 2366.67 330 4.7811
-10 31-18-19 1360.00 214 4.2368
16—17~14 940.00 171 3.6647
13-9-12 680.00 130 3.4872

 

121

TABLE A—11.—-Influence of air flow rate gradient on trans—
port characteristics of air—borne bacteria with 1.0 ft

 

 

 

 

 

 

opening.
Air Flow
Rate Steady—State Mass Concentration Transfer
Difference Transfer Flux Gradient Coefficient
3 3 3 [No./min-ft2
(ft /min.) (No./ft ) (No./min.) (No/ft ) (No./ft3)]
39.3 83—68-82 831.03 305 2.7247
37-32—21 321.00 198 1.6212
33-39-38 392-33 329 1.1925
57-56-61 620.60 368 1.6864
73-58-59 677.67 321 2.1111
54-38-61 545.70 293 1.8625
50-68—51 602.77 315 1.9135
28.7 25-28-29 653.20 271 2.4103
28-35-25 624.80 257 2.4311
23-28—29 568.00 216 2.6296
41-39-34 809.40 311 2.6026
20 57-43-39 1390.00 356 3.9045
39—41—41 1210.00 327 3.7003
60—53-54 1670.00 375 4.4533
67-70—76 2130.00 385 5.5325
10 58—62—50 2266.67 402 5.6385
33—27-32 1226.67 265 4.6289
38-37-47 1626.67 267 6.0924
38—23—29 1200.00 243 4.9383
0 29-26—30 1416.67 291 4.8683
41—43-53 2283.33 363 6.2903
44—48—40 2200.00 456 4.8246
48-59—61 2800.00 479 5.8455
—10 12—17—30 1179.99 168 4.6825
43-40—37 2400.00 380 6.3158
16—32—25 1279.99 162 5.2750

 

122

TABLE A—12.—-Inf1uence of air flow rate gradient on trans—
port characteristics of air—borne bacteria with 0.5 ft

 

 

 

 

 

 

opening.
Air Flow
Rate Steady-State Mass Concentration Transfer
Difference Transfer Flux Gradient Coefficient
3 3 3 [No./min-ft2
(ft /min.) (No./ft ) (No./min.) (No./ft ) (No./ft3)]
39.3 40—42—45 452.97 333 2.7205
59—48-60 595.63 410 2.9055
43-51—62 556.40 440 2.5291
28.7 19-32—20 540.10 197 5.1178
17—40—28 603.50 268 4.5037
56-38—50 1022.40 428 4.7776
47—56—43 1036.60 447 4.6380
20 23-26—21 700.00 235 5.9575
30-19—13 620.00 240 5.1667
36-30-31 970.00 335 5.7910
39-24-30 930.00 341 5.4546
10 34-37-43 1520.00 373 8.1501
49-39-46 1786.67 376 9.5036
19-20-32 946.67 207 9.1465
25-30-27 1093-33 241 9.0733
0 42-45-39 2100.00 474 8.8607
46-45-30 2016.60 433 9.3148
52-29—17 1533-33 382 8.5515
18—22—27 1116.67 242 9.2287
—10 21-21-19 1020.00 298 6.8456
12-13—8 660.00 229 5.7642

 

123

TABLE A—13.—-Influence of temperature gradient on the
transport characteristics of air-borne bacteria at 61

 

 

 

 

 

ft3/min.

Temperature Steady—State Mass Concentration Transfer

Gradient Transfer Flux Gradient Coefficient

3 3 [No./ft2—min

(OF.) (No./ft ) (No./min) (No./ft ) (No./ft3)]
-14 16-13-17 935.33 272 2.2925
20-13—14 955.67 252 2.4985
—12 24—21-20 1321.67 515 1.7109
18—24—26 1382.67 433 2.1288
-11 28-27—33 1789.33 376 3.1726
21-19—25 1321.67 350 2.5175
18—17—20 1100.00 248 2.9569
16-19-20 1100.00 257 2.8534
-10 41-34—43 2399-33 504 3.1737
38-37—38 2297.67 473 3.2384
—6 48—39-56 2907.67 453 4.2791
48-36—58 2887.33 404 4.7646
—5 40-43-41 2521.33 335 5.0176
34-34-38 2155.33 341 4.2138
0 22—21-25 1382.67 189 4.8771
22—27—24 1484.33 170 5.8209
24-22-25 1443.67 154 6.2496
54—50-44 3009.33 405 4.9536
5 29-27-29 1728.33 231 4.9880
29—22—25 1545.33 215 4.7917
19—25—15 1199.67 160 4.9986
30-23-35 1789-33 162 7-3635
10 16—29—18 1281.00 149 5.7315
21—29-19 1403.00 144 6.4954
26-26—21 1484.33 173 6.5970
25—20-24 1403.00 137 6.8273
12 28—30-19 1565.67 118 8.8455
23-20—24 1362.33 117 7.7626
12.5 28-28-21 1423.33 121 7.8421
17—25—27 1403.00 118 7.9266

 

124

TABLE A—14.—-Turbu1ence data at various locations and flow

 

 

 

 

 

 

conditions.

72

/_ u

f Location UT? 11'2 ' E
(ft3/min) (in.) (ftZ/minZ) (ft/min) (%)
61-61 0 2.053 1.432 37.60
58-58 0 1.68 1.295 35.75
50-50 0 1.675 1.285 42.20
40-40 0 1.355 1.162 46.50
30-30 0 0.7503 0.866 46.15
20-20 0 0.419 0.646 48.60
50-20 8 0.025 0.158 11.89
50-20 6 0.0995 0.315 23.70
50-20 4 0.513 0.716 53.75
50-20 2 1.106 1.052 73.80
50-20 1 0.5069 0.711 41.70
50—20 0 0.7858 0.885 40 35
50-20 -1 1.343 1.159 43.10
50-20 -2 0.650 0.8055 27.20
50-20 -4 1.981 1.408 46.00
50-20 -6 1.277 1.128 36 85

20-20 -6 0.0041 0.064 4.8
20-20 -4 0.0096 0.0979 7.36
20-20 -2 0.112 0.3343 25.15
20-20 -1 0.164 0.4045 30.40
30-30 -4 0.503 0.710 37.75
30-20 8 0.2538 0.5035 26.82
40-40 8 0.4186 0.646 25.85
50-50 8 1.161 1.078 35.20
58—58 8 0.437 0.661 18.22
61-61 8 1.9994 1.412 37.03
20-60 8 1.415 1.189 31.68
50-70 0 1.479 1.215 32.65
50-60 0 2.538 1.59 46.65
40—70 0 1.647 1.282 37.30
30-70 0 2.8329 1.68 53.80
40-60 0 1.2095 1.099 35.18
30-60 0 1.942 1.393 49.60
40-50 0 0.675 0.821 29 20
20-50 0 1.4634 1.209 5.10
30-40 0 0.475 0.689 31.40
20-40 0 0.4334 0.6585 35.10
20-60 0 1.2057 1.098 43.90
30-50 0 1.0579 1.027 41.10
10-50 0 0.7823 0.884 47.15
10-40 -2 0.0587 0.2332 30.20

10-40 -6 0 0 0
10-40 0 0.6474 0.8035 50.75

 

125

 

 

000 0 00.0 00.00 000.0 000.0 000.0 000.0 0000.0 0.00-00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 0000.0 0 00-00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 0000.0 00-00
000.0 00.0 00.0 000.0 000.0 000 0 000.0 0000.0 00-00
000.0 00.0 00.0 000.0 000.0 000.0 000 0 0000.0 00-00
000.0 00.0 00.0 000 0 000.0 000.0 000.0 0000.0 00-00
000.0 00.0 00.00 000 0 000.0 000.0 000.0 0000.0 0.00-00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 0000.0 0.00-00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 0000.0 00-00
000.0 00.0 00.0 000.0 000 0 000.0 000.0 0000.0 00-00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 0000.0 00-00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 0000.0 00-00
000.0 00.0 00.00 000.0 000.0 000.0 000.0 0000.0 0.00-00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 000.0 0.00-00
000.0 00.0 00.0 000.0 000.0 000 0 000.0 0000.0 00-00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 0000.0 00-00
000.0 00.0 00.0 000.0 000.0 000 0 000.0 0000.0 00-00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 000.0 00-00
000.0 00.0 00.0 000 0 000.0 000 0 000.0 0000.0 0.00-0.00
000.0 00.0 00.0 000.0 000.0 000.0 000.0 000.0 00-00
000.0 00.0 00.0 000.0 000.0 000 0 000 0 000 0 00-00
000.0 00.0 00.0 000 0 000.0 000.0 000.0 000.0 00-00
000.0 00.0 000.0 000.0 000.0 000.0 000.0 000.0 00-00
000.0 00.0 000.0 000.0 000.0 000.0 000.0 000.0 00-00
0.000 0000 00050 0:00 0005\000 0005\0000 00-00 x 0050 00:0E\0000 0:0ex0000
0 00 0 .0 0.0V 00 00000000 0.0 0

x

 

 

 

 

.mcoHuHUCOO 3O0m 0c0 020000000 mzowp0> p0 0000 :o0mpmamHQ-I.m01< mqm<9

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126

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