ABSTRACT
AIR FLOW CHARACTERISTICS OF A SCALE MODEL CHAMBER

By
Stephen Arthur Weller

lAdequate ventilation of a confined area, is an important requirement
for the good health of its occupants. This investigation was conducted
to determine the air flow characteristics of a scale model air chamber,
equipped with a particular ventilation system. The air chamber was two
feet by eight feet by ten feet. The ventilation inlet consisted of a one
half inch slot located across the tOp of one end. A four inch circular
exhaust outlet was located at t0p center of the opposite end.

Air velocity fluctuations were detected by a hot wire anemometer and
recorded for 126 data points located.on a vertical plane perpendicular to
the inlet at its midpoint. Recordings, of five seconds duration, were
made at each data point for two components and, in several cases, for two
flow rates.

Information on mean velocity, variance of velocity fluctuation, tur-

bulent intensity and dispersion factor of the air at each point was obtained

by means of a statistical analysis of the air velocity records. This infor—

mation was then statistically analyzed to produce profiles, scatter diagrams

and correlations. From this a fairly clear picture was obtained as to the
behavior of the air within the chamber, for the given type of ventilation

system.

Approved 27% X’W

Majér Professor

Department Chairman

 

AIR FLOW CHARACTERISTICS OF A SCALE MODEL CHAMBER

By

Stephen Arthur Weller

A THESIS

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

MASTER OF SCIENCE
Department of Agricultural Engineering

1966

ACKNOWLEDGEMENTS

My sincere appreciation is extended to Dr. D.R. Heldman (Agricultural
Engineering) for the guidance, inspiration and knowledge he provided me
with, as it made this portion of my graduate program both a pleasing and
rewarding experience.

Sincere appreciation is extended to Dr. M.L. Esmay, my major professor
(Agricultural Engineering), for supplying necessary funds for materials and
services and in providing advise and suggestions whenever requested.

Additional acknowledgement is extended to Dr. C.W. Hall, Chairman of
the Agricultural Engineering Department, for his guidance and leadership and
to Professor L.V. Nothstine, my minor professor (Civil Engineering), for the
knowledge obtained from his courses.

The professional services volunteered by my sister, Donna, to type this
thesis was a tremendous help in producing a presentable copy, and is greatly
appreciated.

The patience and support of my wife, Connie, throughout my graduate

education has been a real help and to her I am deeply grateful.

ii

To:

Cornelia, Michael and Maria
Mr. and Mrs. Donald Weller
Mr. and Mrs. Arthur Miner
Mr. and Mrs. Merrill Weller

Mr. and Mrs. Leo Krone

iii

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Chapter
1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . . 2
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . 2
2.2. Characteristics of Ventilation Air Jets . . . . . . . . . 2
2.3. Statistical Methods . . . . . . . . . . . . . . . . . . . 4
3. THEORETICAL CONSIDERATIONS . . . . . . . . . . . . . . . . . . 6
3.1. Flowmetering . . . . . . . . . . . . . . . . . . . . . . 6

3.2. Wire Calibration . . . . . . . . . . . . . . . . . . . . 10
3.3. Air Flow and Turbulent Measurements . . . . . . . . . . . 12
3.4. Velocity Fluctuations . . . . . . . . . . . . . . . . . . 13
3.5. Turbulence . . . . . . . . . . . . . . . . . . . . . . . 13
3.6. Correlation Coefficients . . . . . . . . . . . . . . . . 14
3.7. Eddy Diffusivity . . . . . . .'. . . . . . . . . . . . . 15
3.8. Regression, Standard Error of Estimate and Correlation . 16

4. EXPERIMENTTJ.IPROCEDURES AND EQUIPMENT . . . . . . . . . . . . . 18
. 4.1. Equipment . . . . . . . . . . . . . . . . . . . . . . . . 18
4.1.a. Air Chamber . . . . . . . . . . . . . . . . . . . 18

4.1.b. Venturi Tube . . . . . . . . . . . . . . . . . . 20

iv

4.1.c. Wire Calibration . . . . . . . . . . . .

4.1.d. Air Flow and Turbulence Measurements . .
4.2. Scope of Tests . . . . . . . . . . . . . . . s
4.3. Analysis of Air Flow and Turbulence Measurements

4.3.a. Statistical Analysis . . . . . . . . . .

4.3.b. Profiles . . . . . . . . . . . . . . . .

5. RESULTS AND DISCUSSION . . . . . . . . . . . . . .

5.1. Flow Rate . . . . . . . . . . . . . . . . . . .
5.2. Results of Program TURB . . . . . . . . . . . . .

5.3. Resultant Velocities .

5.4. Profiles . . . . . . . . . . . . . . . . . . . .

5.5. Discussion of Profiles . . . . . . . . . .

5.6. Profile Intensities . . . . . . . . . . . . . . .

5.7. Statistical Methods . . . . . . . .

5.8. Discussion of Tables 5.2 and 5.3 . . . . . . . .

4 5.9. Summary . . . . . . . . . . . . . . . . . . . .

5.10. Discussion of Low Flow Rate . . . . . . . . . . .

6. CONCLUSIONS . . . . . . . . . . . .
7. RECOMMENDATIONS FOR FUTURE WORK . . . . . . . . . . .
APPENDIX . . . .

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . .

Page

20
26
26
27
27
28
31
31
31
34
37
4O
41
43
45
48
49
51
52
53

86

Table

3.1.

5.1.

5.2.

5.3.

LIST OF TABLES

Page
Relation between Reynolds number and discharge coefficient
for a diameter ratio of 1/2 inch . . . . . . . . . . . . . . . 8
Area maximum and minimum . . . . . . . . . . . . . . . . . . . 42
Results of program ANALl for the case of linear correlation . 46
Results of program ANALl for the case of non-linear corre-
lation O O O O O O O O O O O O O O O O O O O O O O O O O O O O 47

vi

Figure

3.1.

4.9.

4.10.

5.1.

5.2.
5.3.

5.4.

5.5.

5.6.

LIST OF FIGURES

Page
A typical calibration curve for a given resistance ratio
with I being the current to hold it fixed as the product
Of pV 18 Changed 0 O O O O O O O O O O O O O O O O O O O O O O 11
Experimental apparatus used for the collection of data . . . . 19
Air chamber inlet . . . . . . . . . . . . . . . . . . . . . . . 19
Apparatus to which probe was mounted . . . . . . . . . . . . . 21
The crank in the left hand controls the left to right
movement while the crank in the right hand controls the

front to back movement . . . . . . . . . . . . . . . . . . . . 21

View at outlet end of chamber showing venturi and
manometer O O O O O I O O O O I O O O O O O O O O O O O O O O O 22

Apparatus used to measure and record air velocity
fluctuations O O O O O O O O O O O O O O O O O O O O O O O O O 22

Calibration curve of venturi tube used in measuring air flow . 23

Calibrationzcurve of hot-wire filament used in measuring
air flow (1 versus T3?) . . . . . . . . . . . . . . . . . . . 24

Calibration curve of hot-wire filament used in measuring
air flow (V versus I) O O O O O O O O O O O O O O O O O O O O O 25

Location of data points in plane under investigation . . . . . 30

A typical correlation curve used in obtaining a dispersion

factor O O O O O O O O O O O O O O O O O I O O O O O O O O O O 33
The resultant angles at each grid point . . . . . . . . . . . . 35
Profiles of resultant velocities which show inlet air jet . . . 38

Profiles of turbulent intensities (horizontal component, left;
vertical component, right). . . . . . . . . . . . . . . . . . . 39

Profiles of dispersion factors (horizontal component, left;
vertical component, right) . . . . . . . . . . . . . . . . . . 39

Typical scatter diagram . . . . . . . . . . . . . . . . . . . . 44

vii

A01.

A.2.

A.3.

A.4.

End view of air chamber

Side view of air chamber .

Details of inlet end .

Details of outlet end

viii

Page
55

56
57

58

LIST OF APPENDICES

Appendix _ Page
A.1. Construction Details of Air Chamber . . . . . . . . . . . . . 54
A.2. Program VENTURI . . . . . . . . . . . . . . . . . . . . . . . 59
A.3.. Program CALIBRAT . . . . . . . . . . . . . . . . . . . . . . . 61
A.4. Program TURB . . . . . . . . . . . . . . . . . . . . . . . . . 63

A.4.a. Subprogram STAT . . . . . . . . . . . . . . . . . . . 69
A.4.b. Subprogram GRAPH . . . . . . . . . . . . . . . . . . . 7O
A.4.c. Sample of Input Data . . . . . . . . . . . . . . . . . 71
A.5. Program ANALl _. . . . . . . . . . . . . . . . . . . . .'. . . 72
A.5.a. Subprogram MATINV . . . . . . . . . . . . . . . . . . 75
A.6. Program ANAL2 . . . . . . . . . . . . . . . . . .'. . . . . . 77
A.7. Program TURB Output . . . . . . . . . . . . . . . . . . . . . 79
A.7.a. Horizontal Component . . . . . . . . . . . . . . . . . 80

A.7.b. Vertical Component . . . . . . . . . . . . . . . . . . 83

ix

1. INTRODUCTION

As stated by Stephan (1960), "Proper ventilation must supply oxygen,
and also dilute and remove carbon dioxide, ammonia, disease organisms and
water vapor without causing drafts or producing an excessively low air
temperature within the room". A requirement of maximum production is preper
environment, which is a product of pr0per ventilation. It is necessary to
control the ambient air conditions in shelters so as to induce a favorable,
response from the birds and result in a high-quality product (Longhouse,
1960; Esmay 1960).

Ventilating systems range from allowing air to enter by means of leakage
around windows, through cracks and under doors to controlled entry through
designed and installed inlets. One inlet system consists of a horizontal
slot located along the top of one side of the room. Within the room, the
exhaust fan causes the air to circulate throughout and finally to be exhausted.
This type of ventilation system was chosen and its air characteristics were
studied.

This thesis was primarily concerned with a study of air movement in a
vertical plane passed perpendicular to the inlet slot and near its midpoint.
This study was carried out in a scale model air chamber and included an
investigation of mean velocity, variance of velocity fluctuations, turbulent

intensity and dispersion factors for the air fluctuations of the given plane.

2. LITERATURE REVIEW

2.1. Introduction

As one reviews the literature, looking for information on the distri-
bution and mixing of ventilation air, he begins to realize that a great deal
of work has been done on free jet streams but not very much on the effects of
enclosures or on air characteristics adjacent to the jet stream.

In and near the jet stream, measurable parameters are fairly well defin-
ed. As one moves farther away from the boundry layer or farther down stream
from the jet inlet, parameters become more difficult to establish.

2.2. Characteristics of Ventilation Air Jets

Parker and White (1965) made a study of velocity profiles, flow patterns,
throw and entrainment resulting from the Kentucky fan-baffle system. The
study was also to determine if relationships similiar to those developed for
free air jets can be applied to the plane radial jets produced by this system.

It is important in ventilation studies to know the degree to which in-
coming air is mixed and modified by the air already contained in the ventilated
space. This can be determined (Parker and White, 1965) from the entrainment
ratio (Ex) which is defined as the quantity of air entrained by the jet air
stream up to any given point along the jet divided by the total quantity of air

flowing from the ventilation inlet. In equation form:

Q - Q
o
where: Ex - entrainment ratio
Qo - air flow (cfm) at the jet inlet

Qx - air flow (cfm) in the jet enve10pe at any distance x from
the inlet

Farguharson (1952) expressed the entrainment ratio in the form

E = Cx/{AE (2.2)

x
where: C a a constant
x . distance from inlet
AR - effective area of inlet

For very long slots Farguharson (1952) has confirmed that the axial

velocity in a free jet falls off according to the equation:

V

—x- = K'2 6.5b < x < 6.5a (2.3)
V x
o
where: x a distance measured along the air stream from inlet (feet)

V = maximum velocity (fpm) at any distance x along the jet
V = velocity of air at the vena contracts (fpm)

a = length of rectangular inlet

b = width of rectangular inlet

K' = is a constant for each particular type of slot inlet

If the jet inlet is in the proximity of walls or ceilings an increase
in throw is obtained (Parker and White, 1965). Also these jet streams will
be drawn to and remain close to that surface (Parker and White, 1965; Becker,
1950; Farguharson, 1952).

Tilley (1964) states that "a jet of air coming from the air inlet into a

room will spread out, unbaffled, at an inclusion angle of between 15° and 20°"

2.3. Statistical Methods
In order to obtain a better understanding of the air characteristics
of a chamber, a statistical description of the turbulent field is required.
Taylor (1921) introduced the basic concepts involved in the statistical
theory of turbulence and then later developed them (Taylor, 1935). In gen-
eral, the statistical concept involves the correlation between simultaneous
velocities at two fixed points or between the velocity of a particle at one
time and that of the same particle at a later time. These are referred to
as the Eulerian and the Lagrangian description reapectively (Frenkiel, 1953).
Statistical aspects of turbulent flow are reviewed by Frenkiel (1953).
The instantaneous velocity usually consists of two parts. They are the mean

velocity 5 and the turbulent velocity u'(t), such that
u(t) - 5+ u'(t) (2.4)

for all t. A measure of the spread of the fluctuating turbulent velocity

u' can be obtained from the variance u'2 i O or the standard deviationi u,2 .

The ratio of such a standard deviation to the mean velocity (when E i 0) is

called the intensity of turbulence and is given by the expression

‘!u'2 /E

Frenkiel (1953) defines the Eulerian longintudinal correlation coeffic-

ient for velocity as:

 

 

(2.5)

 

Theoretically Rx(x) will range from one, when x = 0 and the two points
coincide, to zero, when x - w and there is practically no correlation between
the components of the velocity at the two points.

Frenkeil (1953) also defines the Lagrangian longitudinal correlation

coefficient as:

 

u'(t) u'(t+h)
RtLu(h) - A A (2.6)

[(uytnz ((uywhnz

Derived from Taylor's (1921) theory, Harrington (1965) given

 

 

 

K - u'2 I” R u(h)dh (2.7)
0 tL
or
K - Bu'zf“ R (x)dx (2.8)
o x
where:
K - eddy diffusivity
3 - {F’/41
i - intensity of turbulence.

3.1.

3. THEORETICAL CONSIDERATIONS

Flowmetering

Eckman (1950) gives the following equation for venturi tube flow of

compressible fluids:

where:

 

 

 

2gh (3-1)

flow rate, ft3/sec

venturi discharge coefficient

diameter ratio - d/D

venturi throat diameter, ft

pipe diameter, ft

rational expansion factor

specific volume of gas at base conditions, ft3/1b
specific volume of gas at upstream conditions, ft3/lb
moisture factor at base conditions

moisture factor at upstream conditions

weight density of fluid over manometer fluid, lb/ft3
density of fluid over manometer fluid, lb/ft3

2
acceleration due to gravite, ft/sec

manometer differential, ft

According to Olson (1961) a compressible fluid expands in passing through

the throat of the venturi tube. Hence, the effect is to reduce the flow

rate of the fluid for given initial conditions and pressure drOp as compared
with the flow rate if incompressible flow were assumed. At low flow rates,
such as used in this experiment, the error produced in assuming incompressible
flow will not be very large. Kunze (1964) stated that it was suggested in the
AE 430, Laboratory Exercise II, entitled "Measurements of Flow of Gases" that

the equation

 

28h (Y - Y )
v - K m f (3.2)
m D

 

be used where K - 0.258 and Vm has units of ft/sec.
Eckman (1950) gives the following equation for venturi tube flow for

incompressible fluids:

0

2 2
ND 8 28h(Y - Y )
q _ CVT m f (3.3)

41-84 0
3

p - density of flowing fluid, lb/ft .

 

 

 

where:

Equation (3.3) may be written

 

28h (Ym - Yf) (3.4)

 

 

m-F

where q "Von If CVTBZ/ l-B , then equation (3.4) is equivalent to equation

(3.2) if B - .5 and CVT - 1; K = 0.255.

The fluid over the manometer fluid is the same as the fluid flowing
through the venturi, thusyf =(). The liquid used in the manometer has
a specific gravity of 0.797. However, its calibration is such as to read
"h" directly in inches of water. This then is interpreted to be equiva—
lent to the situation where water is actually used as the manometer fluid
and thus would represent the density of water at the Operating temperature.

For most accurate results, CVT should be obtained from a calibration
curve for the particular venturi tube. However, Eckman (1950) states that
”Normally the discharge coefficient is greater than 0.90 and less than 1.0."
Daugherty (1954) states that "Unless specific information is available for

a given venturi tube, the value of C may be assumed to be about 0.99 for

VT
the large tubes and about 0.97 or 0.98 for small ones, provided the flow is
such as to give reasonable high Reynolds numbers." From the graph on page

306 of Pao (1961) Table 3.1 is formed, relating Reynolds number and dis—

charge coefficient, for a diameter ratio of 1/2.

Table 3.1. -- Relation between Reynolds number and

Discharge coefficient for a diameter ratio of 1/2

Reynolds number discharge coefficient

4

2 x 10 .968

3 x 104 .974

6 x 104 .981

1 x 105 .984

4 x 105 .988
6

l x 10 .989

According to Eckman (1950), Reynolds number is directly preportional

to flow rate and is determined from

RD _ fl. £!L_

n uBD

where: u - absolute viscosity of flowing fluid, lb/ft-sec. For example,

let p - 0.0823 1b/ft3 - density of air at 83°F dry bulb and 63°F wet bulb,

u - 0.0000124 1b/ft-sec at 83°, (page 20 of Henderson (1955)), B = 0.5, D = 4
in. and q - 1.5 ft3/sec.

Then

3_ ,(,0723)(1.§)g a 4
RD ' n (0.0000124)(.5)(4/12) 6'68 x 10

From the above tabulation, this corresponds to a discharge coefficient of
about 0.981. For the above conditions ym a 62.19 1b/ft3 and yf - p. Let

g - 32.174 ft/sec2 and h - 1.0 in.

 

q - ung9) (0.981)(1/4) 2(32;l74)(11(92:19 - .0723) _ 1.5 ft3/sec

4 Jl-l/l6 (.0723)12

Let h = .5 and if q = 1.0 ft3/sec, then RD = 4.45 x 104 which corresponds

to CVT - 0.977. This in turn gives a q - 1.06.

The flow rates used in the above example are approximately to those used

in the laboratory. Over this range of flow rates, C could be approximated

VT

by 0.979 with only a small error resulting. Since the assumption of incom-
pressible flow (top of page 7) would lead to a flow rate that is too large,

it is suggested that a C of 0.95 be used as a means of compensation.

VT

10

3.2. Wire Calibration

A hot-wire anemometer is a rapid-response instrument used to measure
the velocity of air or other fluids. Its Operation is based on the cooling
of an electrically heated wire filament, as measured by the change in elec—
trical resistance of the wire. The cooling of the wire depends upon stream
velocity, temperature and pressure. By Operating the wire at a fixed resis—
tance ratio, (Flow Corporation, Bulletin 37, page 11) any significant effect
of stream temperature on average velocity can be eliminated. For streams
where the Mach Number is less than .3, the wire heating current I, where I
is the current required to hold the resistance ratio fixed, is then depen-
dent only On the product of pressure p and velocity V.

Each wire used, must be calibrated by relating known values of p and V
to I. (A typical calibration curve is shown in Figure 3.1.) The plot Of
12 versus pV is substantially a straight line up to a Mach Number of about
.3, hence a calibration curve can be Obtained from just two pV to I relations.
This linear portion is also correct over a wide range of pressures.

If wide ranges of temperature occur, then the entire curve translates
vertically. The distance of translation measured in percentage Of the inter-
cept is .9 times the percent change of the absolute stream temperature. If a
calibration curve was Obtained for a stream temperature of 530°R and the tem—
perature is actually 540°R, then the correct calibration curve should be shifted
downwards by (10/530)(.9)(100) - 1.7 percent of the intercept as less current

would be required to maintain wire temperature.

‘ ll

  
 

resistance ratio = 1.3

 

 

(a?

Figure 3.1. -- A typical calibration curve for a given
resistance ratio with I being the current to hold it
fixed as the product of pV is changed.

For the two point calibration curve, the first point that can be used
is the intercept point. At this point I has the value required to maintain
wire temperature at zero stream velocity. The second point must be based
on a known velocity and pressure.

The second point can be obtained by measuring I with the wire perpen-
dicular to a known stream velocity. By placing a pitot tube near the wire,
parallel to the direction of flow, the stream velocity can be Obtained.
According to Eckman (1950), equation 3.5 can be used to obtain stream velo-

city.

 

Vl = CPT «(Ym - yf)ul VZgh (3.5)

Equation 3.5 can be written in the form

0

12

 

v1 - cPT{2gh(ym - ypr (3.6)

where CPT is the velocity coefficient and has a value between 0.98 and
1.02 for a pitot tube with a long-Opening extension. A value of CPT = 1
will be used.
3.3 Air Flow and Turbulent Measurements

From the calibration curve Of Figure 3.1 a curve Of pV versus I can
be constructed for each constant resistance ratio. If p is assumed to
remain constant, then a certain fluctuation in V can be determined from

this curve if.the equivalent change AI in I were known. According to

the Flow Corporation Bulletin (1958), AI can be obtained from

 

 

Zie
AI - I 1 - if - 1 (3.7)
Is
is
where: I - wire current, ma

1 - square-wave current, ma

eis - zero to peak square wave amplitude, volts

eif - voltage deflection due to velocity fluctuations, volts.

The square-wave current i can be Obtained from

3.05

' 1 + (B)(N)/4OO (3.8)

i

where: B - bridge null reading

N - resistance ratio used

3.4. Velocity Fluctuations
The equations of section 3.3 pertain to the constant current method.
That is, the heating current to the wire is kept constant and the voltage
across.the.wire is examined. If the voltage fluctuations are tO represent
velocity fluctuations then certain conditions must be met based on the
limitations Of the instrument being used.
The assumptions are as follows:
1. The velOcity component is perpendicular to the wire axis.
2. The distortion due to large slow fluctuations does not have
an adverse effect on the desired results.
3. The static pressure remains constant; p = constant.
3.5. Turbulence
The instantaneous velocity at‘a given point A can be divided into two
parts, the mean velocity‘5"and'the turbulent velocity u'A(t), such that

A

uA(t) - E + UA(C)

A

for all t. Consider in a turbulent field a Set of orthogonal axes 0xyz
with the axis 0x parallel to the direction of a constant mean velocity.
Let u, v,‘w denote the three components Of the instantaneous velocity vec—
tor on the x,.y, and z axes respectively. Since 0x was chosen parallel to
the mean velocity, we have 6 - constant, 5 B 0, §'- 0, and the components
of the turbulent velocity are u' - u — E, v' - v and w' = w.

The values of the variances u'z, v'Z, w'2

 

or their square roots, the

 

standard deviations {n.2, [7,2, EJ are a measure of the Spread of the

fluctuation turbulent velocities u', v', and w'. Frenkiel (1953) defines

14

the ratio of such a standard deviation to the mean velocity (when G # 0)
as the intensity of turbulence. There are three such intensities. They

are as follows:

longitudinal intensity Of turbulence

2. transverse intensity of turbulence
w'2

3. -jf*'- transverse intensity of turbulence
u

3.6. Correlation Coefficients

Correlation is the degree of relationship between two or more vari-
ables. Frenkiel (1953) gives expressions for two correlation coefficients
used in relation to turbulent diffusion. The first is the Eulerian corre-
lation coefficient and is given by the ratio

axe.) =- “8 “Q (3.9)
1;??? [:75
P Q

The two points P and Q are on a line which is parallel to the direction of

 

 

the mean velocity and separated by a distance x = x2 — x1.

ous longitudinal components of the turbulent velocities at the two points

The instantane-

are ué(t) and ué(t).

The second is Lagrangian correlation coefficient and is given by the

ratio

 

u'(t) u'(t +'h)
R u(h) - A A ~ (3.10)
CL l

{(uycnz 1mg: + h>>2

 

During the time interval h, A has moved from, say, point P to point P

1 2'
Neither Of these two forms are satisfactory for the experimentation being
considered as the point Of measure must be fixed.

Frenkiel (1953) suggested that an Eulerian time correlation coefficient
RE(£) can be defined in a manner similar to equation 3.9 which would describe

the correlation between the turbulent velocities at the same point, but at

two different times 5 and E + t. This coefficient would have the form

 

U'(§) U'(E. + Q
u'zm

° (3.11)

RE(t) -

3.7. Eddy Diffusivity

Derived from Taylor's (1921) theory, Harrington (1965) gives

,2

m u
K = u g RtL (h)dh (3.12)

as the expression for eddy diffusivity. Since measurements will be made in
an Eulerian frame Of reference it will be necessary to substitute RE(t) for
RtLu(h)’ where h - St. The eddy diffusivity becomes

K - eu'zngE(t)dc (3.13)

16

{7? (3.14)

where: B I EI-

and i is the intensity Of turbulence.
3.8. Regression, Standard Error of Estimate and Correlation

It is often desirable to Observe and measure the association which occurs
between two statistical series. If the two series are plotted with the inde—
pendent variable On the x axis and the dependent variable on the y axis, the
result is known as the scatter diagram.

If the two series are related, the plotted points will follow a definite
line Of movement. The trend or direction of this movement may be approximated
with a curve known as the line of regression and may be of the form:

1. YO I a + bX
2. Yc I a + bX + cX2

A measure of the variation or scatter about the line Of regression is

given by the expression (Arkin, 1963)

3y -' J£(d2)/N (3.15)

where: Sy I standard error of estimate

d I Y - Y
c

Y I actual values

Y I theoretical values obtained from the equation for the

line of regression

N number of points
One standard error of estimate will include 68% of the cases when measured
off plus and minus about the line of regression if the distribution is a

normal one.

17

The standard error of estimate is a measure of the degree of association
between two series but its size is expressed in terms Of the orginal unit of
the Y variable. A comparative measure of association, which is independent
of the original unit of the Y variable, is termed the coefficient of corre-
lation r for the linear case and the index of correlation p for the non-linear
case. They are defined by the expression

8 2
1 _ L2 (3.16)

o
Y

where: 0y I variance of the Y values.

4. EXPERIMENTAL PROCEDURES
AND EQUIPMENT

4.1. Equipment

Apparatus for the collection of data (Figure 4.1) was set up in a
large room with a temperature of 75° I 3° F and a relative humidity which
varied with weather conditions.

4.1.a. Air Chamber

An air chamber, with inside dimensions of two feet by eight feet by
ten feet, was constructed, to a quarter scale, to represent a "ventilation
section" of a poultry house with inside dimensions of 8 feet by 32 feet by
40 feet. All inside surfaces, except one side, were constructed of 1/4
inch plywood and held in place by a rigid frame (see Appendix A.1. for
construction details). The front side, which was parallel to the vertical
plane being sampled, was constructed of 1/8 inch plexiglas to allow for a
visible view of apparatus located within the chamber.

An inlet, measuring 1/2 inch by 8 feet, was constructed at the left
end at ceiling level. This inlet (Figure 4.2) ran parallel to the ceiling
and was designed with a 3-5/8 inch approach, constructed from two parallel
boards set 1/2 inch apart. The purpose Of this was to produce an air stream
which was parallel to the ceiling on entry into the chamber.

An outlet, measuring four inches in diameter, was constructed at the
right end with its center at the horizontal midpoint and six inches down
from the ceiling. TO this outlet a two foot length of four inch diameter
tubing was connected. This was in turn connected to the exhaust fan

(Figure 4.1) with an adjustable air flow.

18

1

 

Figure 4.1. -- Experimental apparatus

used for the collection of data.

 

Figure 4.2. -- Air chamber inlet.

19

20

Inside the air chamber, an apparatus was constructed to which the hot-
wire probe could be mounted (Figure 4.3). This apparatus provided for two,
horizontal, directional movements Of the probe to be made from outside
(Figure 4.4) the chamber and a third, or vertical, movement with the inlet
end Open. The two horizontal movements could be monitored from outside the
chamber. This allowed for free movement of the probe to any location in
the front half Of a horizontal plane. When a horizontal plane of different
elevation was desired, the chamber was Opened and the probe adjusted.
4.1.b. Venturi Tube

A venturi tube, with a large diameter Of four inches and a throat dia-
meter of two inches, was used as a means of determining the flow rate of
air through the chamber. To the venturi was connected a manometer (Figure
4.5) to obtain the pressure differential of the venturi. Using equation
3.3 a computer program (see Appendix A.2 for program description) was
written to generate data required to form a calibration curve of the ven-
turi (Figure 4.7).

4.1.c. Wire Calibration

The wire filament used to obtain air flow and turbulence data was cal-
ibrated with the use Of a wind tunnel, pitot tube, manometer and hot—wire
anemometer. The data obtained were used with program CALIBRAT, (see Appendix
A.3 for program description) which then produced values for a calibration

curve of the given wire filament (Figure 4.8 and 4.9).

 

 

Figure 4.3. -- Apparatus to which

probe was mounted.

 

.1

‘
llii

.4 .

 

Figure 4.4. -— The crank in the left hand controls the
left to right movement while the crank in the

right hand controls the front to back movement.

21

 

Figure 4.5. -- View at outlet end Of chamber

showing venturi and manometer.

 

Figure 4.6. -- Apparatus used to measure and

record air velocity fluctuations.

22

DISCHARGE - CFM

140

120

100

80

60

40

20

23

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.5 1.0 1.5 2.0

MANOMETER DIFFERENTIAL--IN.

Figure 4.7. -— Calibration curve Of venturi

tube used in measuring air flow.

2.5

DISCHARGE - CFM

140

120

100

80

60

40

20

 

23

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.5 1.0 1.5 2.0

MANOMETER DIFFERENTIAL--IN.

Figure 4.7. -- Calibration curve Of venturi

tube used in measuring air flow.

2.5

24

 

 

 

 

 

 

 

 

 

 

10000
8000 P”/////,!/’//////¢
6000
S 12 - 129.801'p_v + 6123.06
:4! RESISTANCE RATIO I 1.3
: PRESSURE p - 1
0L4
4000
2000
0
0 10 20
1pv -- V(FPM)
Figure 4.8. -- Calibration curve of hot-wire filament

used in measuring air flow. (12 versus 1pV)

30

26

4.1.d. Air Flow find Turbulence Measurement

A constant current hot-wire anemometer (Model HWB NO. 216 by Flow
Corporation, Arlington, Mass.) was used as a means Of converting air vel-
ocity fluctuations into voltage fluctuations. These voltage fluctuations
were recorded on Moseley X—Y recorder (Figure 4.6). Each recording repre-
sents a five second history of a given point for a given flow component.
Each recording was then divided up into 100 equally spaced intervals. A
reference was then chosen to ensure that the amplitude at each interval
end point would be greater than zero as this was a requirement of program
TURB. The relative amplitude for each of the 101 points was punched on
data cards and represents a "data set". Values for wire position, square
- wave voltage, null reading, voltage amplification factor, mean current,
resistance ratio and wire calibration information were recorded for each
"data set". This process was carried out for each point for two flow com—
ponents.

Program TURB (see Appendix A.4 for program description) was then
written, using the equations of section 3.3 through 3.7, to analize these
data and to produce for each "data set" a mean velocity, a variance of vel-
ocity fluctuations, a turbulent intensity and a disperion factor. This
information was printed and punched out for further analysis.

4.2. Scope Of Tests

The investigation of air fluctuations within the air chamber was limited
to a single vertical plane, perpendicular to the inlet and six inches in
front of the center plane. This plane was marked off into a grid of seven

rows and 18 columns (Figure 4.10).

27

It was assumed that air flow, within the air chamber, parallel to the
inlet was negligable. The probe was then given two orientations at each
grid point so as to record a five second history of both the horizontal and
the vertical flow component, for a given air flow rating.

At an air flow of 93.5 CFM, recordings were taken at each grid point
for each orientation. However, at an air flow of 61.7 CFM, recordings were
taken at just a few grid points (Figure 4.10) near the inlet and only for the
horizontal component.

4.3. Analysis of Air Flow and Turbulence Measurements

 

The output data from program TURB were analyzed by the CDC 3600 computer
using two different programs. There were programs ANALl and ANALZ. From
these programs the following were obtained:

1. resultants of the velocity components,

2. scatter diagrams of two or more statistical series
3. lines Of regression

4. correlations between the statistical series

5. profiles of the statistical series

The features of these two programs are described below.
4.3.a. Statistical Analysis

Program ANALl (see Appendix A.5 for program description) was written to
accept and to analyze the punched output data Of program TURB. These data
consist of four statistical series for each of the two components. From these
data a nineth series was produced by determining the velocity resultant of the
two component velocities. The angles these resultants make with respect to a

horizontal position are also determined.

28

Considering any desired groups of two of the nine statistical series,
program ANALl will
1. produce a scatter diagram,

2. approximate it with a linear and a non-linear line of

regression, and
3. determine a correlation factor.

For the scatter diagrams, the range Of each statistical series was
determined and then divided up into the proper number of steps for plotting
on a computer output page. Each division Of the two ranges was related to
a corresponding row and column Of a storage array. The respective pairs of
values of the two series were then related to their prOper row and column
Of the storage array. At the proper location in this array, an asterisk is
placed to represent the corresponding pair. After all pairs have been trans-
ferred to an asterisk in the array, the array is printed out along with the
value of each row and column.

4.3.b. Profiles

It would be very desirable to be able to plot, on a grid (Figure 4.10),
an indication Of the value of the statistical series being considered. Pro—
gram ANAL2 (see Appendix A.6 for program description) was written to do this.
The values Of a given series are divided up into five equal subranges and
zero. The greater the value, the darker will be the mark printed at the pro—
per grid location. A value Of zero, will be printed as a blank. After all I
grid locations have been considered, the profile is printed out (see section
5.4 and 5.5).

In order to Obtain more information about the series, only the values

 

29

in the lowest range were considered. These values were then divided into five
more equal subranges and another profile was obtained. This profile will yield

information about the lower intensities found adjacent to the inlet jet.

30

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5. RESULTS AND DISCUSSION

5.1. Flow Rate

The flow rate, measured at the venturi, was 61.7 CFM and 93.5 CFM. Since
the air chamber had a volume Of 160 cubic feet, there would be an air change
every 2.59 minutes at the lower rate and every 1.71 minutes at the higher rate.
At a full scale Of 10,240 cubic feet and allowing 1.25 square foot per bird,
this would correspond to a flow rate of 3.9 to 5.9 CFM per bird. It was on
this basis that the above flow rates were chosen.
5.2. Results of Program TURB

Intensity of turbulence was defined (section 3.5) as the ratio of the
standard deviation Of the velocity component being considered to the constant
mean velocity. In the air chamber used there was no one directional, constant,
mean velocity. A single orthogonal axies 0XYZ could not be chosen to ensure
that both 3 and w be equal to zero. As a result it was decided to use in
place of the constant mean velocity, the mean velocity Of the component in
u

question. The new ratios thus obtained will be defined as "turbulent intensity

and are as follows:

2

l

TIx I E longitudinal turbulent intensity (5.1.a.)
u

TIY I J v'2 transverse turbulent intensity (5.1.b.)
G

31

32

(:77

TI I —

 

 

_ transverse turbulent intensity (5.1.c.)
w
Eddy diffusivity is given by equation 3.13. Using the definition of turbu—

lent intensity given by equation 5.1 and the coefficient of equation 3.11,

equation 3.13 can be written as follows:

2 ,
DPx - Bxu' gtREX(c)dt (5.2.a.)
- :2 t
2 t
DFZ - BZW' { REZ(t)dt (SeZoCo)

where Bf is defined by equation 3.14. The expression of equation 5.2 will
be defined as "dispersion factors".

The interval of time over which the integral was taken was chosen to
be one half of the fluctuation history. The interval chosen was somewhat
arbitrary but was influenced by the behavior of some of the correlation
coefficient curves. A correlation coefficient curve (Figure 5.1) should
start at a value of one and, theoretically, decay to a value of zero. The
area below this curve is given by an integral of equation 5.2. In practice,
this curve decays by means of a damped oscillation. Therefore, the negative
areas should contribute in a positive sense to the forming of the values of
the integral. In some Of the graphs that were produced, it was Observed that
near the center of the interval there was a slight increase in oscillation
amplitude. It was felt that this extra area should not be included and hence

a 50% factor was used.

33

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OH pow: o>uao coaumamuuoo Hmoammu 4 II .H.m musmfim
0mm II mzHH
0.0 0.m 0.~ 0.H 0.0
3!?
«JW
4‘,
i

 

 

 

 

 

 

 

 

 

0.0:

«.0:

N.0|

0.0

N.0

«.0

0.0

0.0

0.H

34

As TI apptsnches zero58 approaches infinity. Hence a limit will have
to be set on how small TI can become. This limit was set to 10-6 as any
value Of TI less than this would be zero as velocity fluctuation amplitudes
of such a small magnitude could not be interpreted from the recordings.

After making the above modifications in program TURB, it was used to
obtain a value for mean velocity, variance of velocity fluctuations, turbu-
lent intensity and dispersion factor for each "data set" (page 26). These
data were punched on cards, as output from program TURB, and analyzed. A
complete tabulation Of the output data of program TURB is contained in
Appendix A.7.

5.3. Resultant Velocities

The X and Y component of mean velocity was converted to a resultant and
an angle with respect to the X axis using program ANALl. The angles made by
the velocity resultants are shown in Figure 5.2. The directions of the resul-
tants are not definitely known, but based on some preliminary smoke experi-
ments, the orientations shown were chosen for illustration.

Several of the angles appear to be in error, especially locations 1—18,
2-17, 6-4 and 7-15. Because Of the low velocities a small change in one of
the components would have a large effect on the angle of the resultant. This
error could have been caused in particular by fluctuations in discharge rate,
by incorrectly reading the value Of mean current displayed on the anemometer,

or by an incorrect value of square wave voltage, e13.

 

35

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.17

 

 

 

 

 

 

 

 

 

 

 

 

 

A

A

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36

Manometer readings at the venturi indicated a fluctuation in discharge
rate of i'ZCFM. These fluctuations were sporadic and gave the impression
that there was a weak scale turbulence at the entrance to the outlet pipe.
The effect that this had on the air flow within the chamber is not known.

A history of mean velocity of more than five seconds might show this effect,
but since a means was not available for making a continuous recording of.
more than five seconds, this effect was not investigated.

If this fluctuating flow rate were to cause a variation in air velocity
in the chamber, it could effect the angle of the resultant. If the mean
velocity of an X and Y component were established at a time Of low and high
fluctuation, respectively, then the resultant angle would be too large as
at location 1-18.

A greater source Of error extends from the reading Of the value of mean
current displayed on the anemometer. TO obtain this reading, adjustments of
the bridge resistance are made to Obtain a zero reading on the galvanometer.
Since the air at the hot wire filament is turbulent, the galvanometer needle
will tend to oscillate about the zero mark. If the amplitude Of the turbu—
lent oscillation is small, when compared tO the mean velocity, and if it has
a high oscillation rate, then the mean setting can be Obtained very accurately.
However, if the oscillation amplitude is large, with respect to the mean vel—
ocity, and if the rate of oscillation is low, then the galvanometer needle
oscillates rather wildly about the zero setting. When this occurs it is very
difficult to judge what the mean setting should be. Since most of the read-
ings were made under these adverse conditions it is believed that this is the

reason for most of the inconsistencies of Figure 5.2

37

When the oscillation amplitude becomes large, with respect to the mean
velocity, and the oscillation rate is slow, the X—Y recording may not repre-
sent the true turbulent history Of the time of recording. Such large scale
oscillations cause the anemometer to operate in a nonlinear mode causing
distortion of the recording. Since the above conditions existed in some
degree, at all points of measurement, it is felt that the results will still
give a good indication of what is happening within the chamber.

Another source of error is in the establishment of square wave voltage,
e

From equation 3.7 it can be seen that e inversely affects AI, from

is' is

which velocity is Obtainedo As eis is increased AI becomes smaller and thus
the associated velocity is less.

There are many factors which may have caused errors in the recordings
that were made. It is believed that the three listed above were the main
ones and any others that may have existed would be insignificant in relation
to the above.

5.4. Profiles

Using program ANAL2 a profile of the resultant velocities (Figure 5.3),
turbulent intensities (Figure 5.4) and dispersion factors (Figure 5.5) were
produced. There is an upper and lower profile for each of the above three
sets. The upper profile represents the range of values divided up into five
equal subranges and zero. Zero is represented by a blank. The lowest range,
which includes the samllest number greater than zero, is represented by a -.
In order, the highest ranges are represented by (—,I), (-,I,L), (—,I,L,H) and
(-,I,L,H,K) overprint. ’

The lowest range, those represented by a -, is further divided into five

equal parts. Each part is represented by a dot in the lower profile. Again

38

all zero are represented by a blank.
Four profiles are shown in each Of Figure 5.4 and 5.5. The left and
right profiles represent the horizontal and vertical components, respectively.

All profiles shown are for an air flow of 93.5 CFM.

IHIBIELLIE—II -----
——IILIIIIII§I -----
-------- 1111-;;--—
--— --11

 

 

 

 

..........l..;-IIP
--...........EIIIE
—-II-lLl....-..-II
--II----IIII££II..
----II—£II----—I--
------ {Ill-I-I-III

Figure 5.3. -- Profiles of resultant velocities
which show inlet air jet.

IIIIIILIIIEIIEE—-I
EIIIIIIIEHIILIII—I

- -IIIIIIIIII—II—
-------- I—IIIE——-

 

 

OOOOOOOIOOOOOOOLEI

I -..........l——.
----- LII.-....LII
------ II-I-III.---
- l—--—IIl.--ILII

I---IlII---II

IIIIHIEIIIIII-E---
-ILIIIEEIIII--I---
-I£lIIII-I--EEI

 

.............l.I-I
l...........ll.EHE
--......-.EI...
II-I-EE.III.IIHE
I.BEIIL.IIEIIII
III II .IBE..EL
IIIII-IIII-I-II

Figure 5.4. -- Profiles of turbulent intensities.

(horizontal component, left; vertical component, right)

 

 

 

 

 

 

 

 

 

I'll}!
; _____
e e o e o om--; -----
--;;emniii -----
- ----IIIII------

 

 

 

 

 

IIIII

; -__
.....LIEEBI ------ I
-—--EE.IBEEEI—--E-

 

 

 

Figure 5.5. -- Profiles of dispersion factors.

(horizontal component, left; vertical component, right)

40

5.5. Discussion of Profiles

All three figures (Figures 5.3, 5.4 and 5.5) indicate that air is
entering at the upper left and fanning out as it moves across the chamber.
These figures indicate that there is a boundry to this fanning and can be
calculated to be roughly 6° from horizontal which would give an inclusion
angle of 12°. 12° is a little less than the 15° given by Tilley (1964) but
if attraction by the ceiling is considered, (Becker, 1950; Farguharson, 1952;
Parker and White, 1965) then 12° is very acceptable.

Another common Observation, is the lack of activity in the lower left
region of the plane. There the air is fairly still with low velocities,
no measurable turbulence and hence no dispersion. This would indicate a
problem area for this type of ventilation system.

In the other areas, conditions are not very well defined. The highest
determined velocity resultant was only 108 feet per minute. But even at
these border line measuring conditions, a better understanding of what is
happening can be Obtained.

For example, in the region bounded by the ceiling and grid row four
and by grid column seven and thirteen, the outside air has mixed fairly well
with the inside air and will now be mixed in varying proportions throughout
the chamber and exhausted. Just how well this air is mixed throughout the
chamber is not completely answered but it is known that it is poor in the

lower left region.

41

Figure 5.2 and the lower profile Of Figure 5.3 indicate that as
the inlet air fans out, after entry into the chamber, the lower portion
reaches the floor at about the midpoint. Here a small portion is drawn
around to the left to circulate through the lower left region. The rest
circulates through the lower right region and then is exhausted.
5.6. Profile Intensities

The plane was divided into four areas as follows:

1. area 1 - rows 1—3, columns 1-9.
2. area 2 - rows 1-3, columns 10-18.
3. area 3 - rows 4-7, columns 1-9.
4. area 4 - rows 4-7, columns 10—18.

Table 5.1 gives the maximum and minimum value for each of the two velocity
components, for the velocity resultants and for the two components Of
velocity variances, turbulent intensities and dispersion factors of the
four areas.
Table 5.1 indicates, as did the profiles, that conditions were not
very uniform within the air chamber. The largest values were found in
area one at the inlet, as expected. These large values extended across
into area two, indicating that most of the activity is in the upper portion
Of the plane as would be eXpected since it contains the inlet and outlet.
Table 5.1 also indicates that isotropic turbulence does not exist as
the magnitudes of the variance of the horizontal mean velocities and of
the variance of the vertical mean velocities are not equal. It can be seen

that the horizontal component is much greater.

42

Table 5.1. —— Area maximum and minimum.
Variable Area High Low
horizontal velocity (FPM) 1 105.7318 0.0912
, 2 43.2137 0.3695
3 18.6140 0.0914
4 27.7150 0.3669
vertical velocity (FPM) 1 28.5066 0.0912
2 16.0486 0.3659
3 4.5523 0.0912
4 . 4.5536 0.0917
resultant velocity (FPM) 1 108.0035 0.1289
2 44.7064 2.7717
3 18.6175 0.3771
4 27.8110 1.1754
horizontal velocity variance 1 2865.6167 0.0000
2 147.8001 0.0058
3 0.1244 0.0000
4 2.2617 0.0015
vertical vleocity variance 1 91.2435 0.0000
2 3.1057 0.0001
3 0.0023 0.0000
4 0.0379 0.0000
horizontal turbulent intensity 1 0.5439 0.0000
2 0.3766 0.0495
3 0.0481 0.0000
4 0.2478 0.0119
vertical turbulent intensity 1 0.3340 70.0000
2 0.2265 0.0198
3 0.1018 0.0000
4 0.2326 0.0000
horizontal dispersion factor 1 7.7683 0.0000
2 0.7729 0.0001
3 0.0151 0.0000
4 0.0581 0.0001
vertical dispersion factor 1 0.3565 0.0000
2 0.0378 0.0000
3 0.0003 0.0000
4 0.0011 0.0000

43

Table 5.1 and Figures 5.3, 5.4 and 5.1 tend to indicate a good
correlation between the variables being considered. The large values
are well grouped, but are the lower values? Section 5.7 and 5.8 will
investigate and discuss this.
5.7. Statistical Methods
Section 4.3.a lists three forms of output produced by program ANALl.
They are as follows:
1. the scatter diagram
2. linear and non-linear line of regression
3. correlation factor
Figure 5.6 shows a typical scatter diagram and the lines Of regression
associated with it. The particular one used as an example, shows the
relation between turbulent intensity and mean velocity for the horizontal
component for an air flow of 93.5 CFM. The coefficients of the equations
describing the lines Of regression and the correlation factors are listed
in Tables 5.2 and 5.3.
The following key is to be used with Tables 5.2 and 5.3:

MV - mean velocity

RV - resultant velocity

VVF - variance Of velocity fluctuations
TI - turbulent intensity

DF - dispersion factor

Sy - standard error of estimate

r - coefficient of correlation

p - index of correlation

TURBULENT INTENSITY

44

 

0.5

 

0.4

.00

 

 

0.3

 

 

 

 

 

 

 

 

 

 

20.0 40.0 60.0 80.0

MEAN VELOCITY -- FPM

Figure 5.6. -- Typical scatter diagram.

100.0

45
When used, these symbols may have a "vc" or an "hc" as a subscript. "vc"
and "hc" stand for vertical component and horizontal component, respectively.
The left column of each table, indicated which two variables were considered.
The left and right variable, of the column, indicate the Y and X axis Of the
scatter diagram, respectively. The right most column gives a measure of the

degree Of association between the variables listed in the left most column.

5.8. Discussion of Tables 5.2 and 5-3

The correlation coefficients ranged from 0.509 to 0.969 and the index
of correlation ranged from 0.549 to 0.970. A comparison Of the two tables
indicate that in several cases the non-linear trend gave a much more accurate
representation Of the data.

The correlation between the two variance velocity components was 0.969
and 0.970 which would indicate that many Of the resultant angles are Of
similar size. Figure 5.2 shown this to be true. Most of the angles are small
due to a predominate horizontal component. If all the resultant angles were
the same, correlation would be perfect. The more varied the size of the angles
the lower will be the correlation.

Because of the definitions adopted for turbulent intensity and dispersion
factor, it is expected that correlations of the other components will also be
high. For the components of mean velocity, turbulent intensity and dispersion
factor, the correlation coefficients were 0.843, 0.804 and 0.926 and the
indexes of correlation were 0.844, 0.805 and 0.930 respectively. Because Of
the very high linear correlation, it is not expected to have much improvement
in the non-linear case. The small variation in the above correlations is due

to the effect the equations of definition have on therelative scattering of

46

Table 5.2. —- Results Of program ANALl for the

case of linear correlation.

Y I A + BX

Variables
X Y A B r

TI VVF 1.1340-01 2.3191—04 0.509
hc hc

TI VVF 7.0539—02 4.3315-03 0.544
vc vc

VVF VVF -2.0933-01 3.3971-02 0.969

vC hC

TIhC RV 6.1800—02 4.4897-03 0.648

TIVC RV 3.7386-02 2.8167-03 0.644

DFhc RV -4.l636-01 5.0526-02 0.862

DFvc RV -l.4333-02 1.7658-03 0.779

DF TI -2.2698-01 4.5299+00 0.535
hc hc

DF TI -1.1293-02 3.0072—01 0.562
vc vc

TI TI 1.6388-02 4.9233-01 0.804
vc hc

TI MV 6.4425-02 4.5344-03 0.638
hc hc

DF MV —3.9622-01 5.1667—02 0.860
hc hc

DF MV -l.3288-02 7.1004-03 0.829
vc vc

MV MV 3.2413-01 2.2918-01 0.843
vc hc

DF DF -l.0839-04 3.5831-02 0.926
vc hc

TI MV 4.5253-02 9.6590-03 0.604

VC

VC

47

Table 5.3. -— Results Of program ANALl for the

case Of non-linear correlation.

Y=A+BX+CX2

Variables
Y X A B C

TI VVF 9.9257—02 6.6748—04 -l.9355-07
hc hc

TI VVF 6.3465-02 1.3887-02 —l.3058—04
vc vc

VVF VVF -3.2665-01 3.7583-02 -1.6053-O6
vc hc

TIhC RV 3.5882-02 8.0278—03 -4.3879-05

TIVC RV 3.7084-02 2.8580—03 -5.1205-07

Dic RV 1.7926—02 —8.7666-03 7.3538-04

DFVC RV 1.7835—03 —4.3459-04 2.7289-05

DF TI -8.3606-02 l.4750+00 6.8946+00
he he

DF TI 3.7646-04 —4.3546—02 l.l494+00
vc vc

TI TI 1.9165—02 4.3315-01 1.3355—01
vc hc

TIhC MVhC 4.0811-02 7,934.03 - —4.4229—05

TI MV 4 4231-02 1.0304-02 -3.l708-05
vc vc

DF MV 1.0310-02 -7.6229—03 7.6141—04
hc hc

DF MV 2.8346—03 —3.0708—03 5.0021-04
vc vc

MV MV 5.1454—01 2.0141-01 3.5664-04
vc hc

DF DF 1.3143-03 2.4749-02 1.6865-03
vc hc

0.638
0.664
0.970
0.683
0.664
0.962
0.879
0.549
0.602
0.805
0.671
0.604
0.956
0.968
0.844

0.930

48

the points. For example, the equations for dispersion factor had a tendency
to force a tighter scattering pattern while the equations for turbulent inten-
sity tended to amplify the scattering. In any case the effect was small.

The correlations between unlike variables were low with one important
exception. The correlation between mean velocity and dispersion factor was
high. Since it was assumed that the dispersion factor was a measure of air
mixing, the above correlation would imply that the greater the velocity, the

greater the mixing.

5.9. Summary
Figures 5.3, 5.4 and 5.5 and Table 5.1 show that the lower left region

below the inlet has very little air movement. There the air velocity was
the lowest of any place in the air chamber and the air fluctuations were
too small to be measured. As a result the turbulent intensity and dispersion
factor were zero. This would tend to indicate that this region was poorly
ventilated.
From the scatter diagrams, that were produced at the time the data of
Tables 5.2 and 5.3 was obtained, the following was observed:
1. At points Of high velocity, there was also high turbulence
and dispersion.
2. There were points Of low velocity and moderately high
turbulence.
3. Points did not exist in which there was low velocity and

moderately high to high dispersion.

49

The above observations were supported by the correlations of Tables 5.2
and 5.3. The correlation between velocity and turbulent intensity was low,
but between velocity and dispersion it was very high.

From this study it cannot be concluded if ventilation is adequate or
not. This would depend on the requirements of the occupants. However, it
was shown what conditions existed in the vertical plane being studied. There
was a jet stream of high velocity, turbulence and dispersion in which out—
side air was mixed with inside air. The higher the velocity in this region,
the greater the air will be mixed. From the flow characteristics shown in
Figure 5.2 it can be seem that a portion of this mixed air is exhausted
without first circulating through the lower portion of the chamber. Figures
5.3 show that this mixed air is not distributed uniformly throughout the
lower portion of the chamber.

This study does present a procedure for determining the characteristics
of a ventilation system. It may indicate where problem areas might exist.
From this information a design improvement may be realized. Once an Optimum
system is developed which exhibits desirable characteristics is it then an
adequate ventilation system? This question must be answered based on the
requirements of the occupants.

5.10. Discussion of Low Flow Rate

Up to this point, all discussion has pertained to the 93.5 CFM flow rate.
Because Of such poorly defined conditions, at the lower flow rate Of 61.7,
measurements were taken only in the area Of the inlet. Because of the limited
number of measurements made, it is not possible to adequately relate the two.

There were two important observations:

50

1. An inlet jet again formed and had a similiar inclusion angle.
As before the major activity was confined to this jet.
2. There were larger areas outside the air jet in which air

movement was too small to be measured.

6. CONCLUSIONS

Based upon this study the following conclusions are made:

1.

Air entering through the inlet fanned out forming an inclusion angle
of about 12°. The boundary of this air jet was defined over about
the first third of the chamber.

Most of the activity was in this jet. As expected maximum values of
velocity, variance of velocity fluctuations, turbulent intensity and
dispersion factors were contained within it. In many cases, values
outside Of the jet were negligible compared to values within the jet.
The air in the area just below the inlet is very still, indicating
the possibility of inadequate ventilation. In many locations of
this area, there was no measurable turbulence or dispersion.

There was a correlation as high as 96.8% between velocity and dis-
persion factor. This would indicate a good relation between velocity
and the rate of mixing.

It can not be stated whether ventilation was adequate or not. There
were areas in which it was felt to be inadequate; in particular the
lower left area below the inlet. What is adequate ventilation and
what value of dispersion factor, if any, can be associated with it

cannot be answered, based on this study.

51

7. RECOMMENDATIONS FOR FUTURE WORK

The results Of this investigation indicate the need for additional

work in the following areas:

1.

2.

Investigation between dispersion factor and adequate ventilation.
The same type of investigation as was carried out only at higher
flow rate so as to obtain more definite relationships and hence
produce a clearer picture Of what is happening.

Investigate the assumptions of negligible air velocity in the 2
direction.

Investigate the effects of temperature.

Investigate other ventilating systems

Study the relationships between the scale model and the full scale.

52

APPENDIX

53

APPENDIX

A.1. Constguction Details of Air Chamber

The construction details of the air chamber used are shown in Figures
A.1, A.2, A.3 and A.4. The stand used to support the air chamber was
constructed from fir 2 x 4'3 and 1/2 in AC exterior plywood gussets. The
rigid framing of the air chamber was constructed from white pine 1 x 4'3
and 1/2 in. AC exterior plywood gussets. To this framing was attached 1/4
in. AC exterior plywood forming the top, bottom, ends and back. The front
Of the chamber was formed by attaching 3/16 in. plexiglas to the framing.
Across the top Of the left end, a 1/2 in. inlet slot was formed. At the
right end a 4 in. outlet was provided with its center located 6 in. from

the top and 2 ft. from the front of the chamber.

54

55

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59

A.2. Program VENTURI

Program VENTURI was written for the purpose of obtaining data for

the plotting of a calibration curve for a given venturi (Figure 4.7).

With the assumption of section 3.1 in mind and using equation 3.3,

values Of q(CFM) are produced when given values for the following:

BD I

D I pipe diameter, in.

SD I d I
G I g I
RO I p I
GM I Ym I
CF I yf I
CVT I

CH -

CVT-

venturi throat diameter, in.
acceleration due to gravity, ft/sec2

density of flowing fluid, lb/ft3

density of manometer fluid, 1b/ft3

density of fluid over manometer fluid, lb/ft3

venturi discharge coefficient

change in manometer differential, in.

PN - number of data points desired for plot

A sample of input data is shown below and is explained at the begin-

ning of the program listing.

Sample of input data:

4.0
2.0
32.174
0.0723
62.19
0.0723
0.95
0.1
21.0

OOOOOOOOOOOOOO

60

PROGRAM VENTURI

DATA CARD 1 -1 LARGE DIAMETER OF VENTURlb 2N.

DATA CARD 2 -- SMALL DIAMETER OF VENTURlo 1N.

DATA CARD 3 -- ACCELERATION DUE To GRAVITY. FT/SEC so

DATA CARD 4 -- DENSITY OF FLowINT FLUID. LB/FT CU

DATA CARD 5 -- DENSITY OF MANOMETER FLUID. LB/FT CU

DATA CARD 6 -- DENSITY OF FLUID OVER MANOMETER FLUID. LB/FT CU
DATA CARD 7 -- VENTURI DISCHARGE COEFFICIENT

DATA CARD 8 - CHANGE IN MANOMETER DIFFERENTIAL. IN.

DATA CARD 9 —- NUMBER OF POINTS DESIRED

VALUES FOR THE ABOVE ARE TO BE PUNCHEDQ WITH DECIMAL
POINT. IN THE FIRST TEN COLUMNS OF EACH RESPECTIVE
DATA CARD.

READ ZOOOBDOSDOGOROOGMQGFQCVTQCHOPN I
NIPN

PRINT 201 ‘
PRINT ZOEOBD'SDOGOROOGMOGFOCVT

P183114159265

A3PI*BD*BD/4e/1Q4e

3350/80

F=B*B/SQRT(IO*B**4)

AF=A*F*6OO

F5820*G/120

FFSFG*(GM~GF)/RO

H‘Oe

PRINT‘203

DO 100 I=ION

STGCAF*CVT*SQRT(FF*H)

PRINT 2040H95TG

100 H‘H‘CH

200 FORMAT(FIOoO)

201 FORMAT(*1*)

202 FORMAT‘E2006* PIPE DIAMETERQINe*/E2006* VENTURI THROAT DIAMETER,
CINO*/EZOOG* ACCELERATION DUE TO GRAVITY*/E2006* DENSITY OF FLOW!
CNG FLUID*/E20.6* DENSITY OF MANOMETER FLUID*/E2006* DENSITY OF F
CLUID OVER MANCHETER FLUID*/E2006* VENTURI DISCHARGE COEFFICIENT*/
C7(/))

203 FORMAT(* *99X0*H(IN)*OllX!*Q(CFM)*O/)

204 FORMAT¢3X9F12¢49F17O4)

END

61

A.3. Program CALIBRAT

Program CALIBRAT was written for the purpose of Obtaining data for

the plotting Of two types of calibration curves for a given hot-wire.

With the assumptions of section 3.2 in mind and using equations 3.6,

values for the TV; 12 and the slope of the calibration curve Of Figure

4.8 and values Of V and I for the calibration curve of Figure 4.9 are

produced when given values for the following:

G -
R0 I
GM ..
CF I
CPT I
H .
FIZRO I
Fl I
CV 3

PN 3

8 I
p I
Ym -
Yf .
CPT '
h I:
41 -
O
41 -

acceleration due to gravity, ft/sec2

density of flowing fluid, lb/ft3

density of manometer fluid, lb/ft3

density of fluid over manometer fluid, lb/ft3
inlet coefficient

manometer differential, in.

current at zero velocity, ma

current at velocity calibration point, ma

change in velocity between points considered, in.

number of points considered

A sample Of input data is shown below and is explained at the begin-

ning Of the program listing.

Sample of input data:

32.174
0.0723
62.19
0.0723
1.0
0.0440
313.0
398.4
10.
91.

00000000000000

100
200
20!
202

0000000000

62

PROGRAM CALIBRAT

DATA CARD I —- ACCELERATION DUE TO GRAVITY. FT/SEC SQ

DATA CARD 2 -- DENSITY OF FLOWING FLUID. LB/FT GU

DATA CARD 3 -- DENSITY OF MANOMETER FLUID. LB/FT CU

DATA CARD 4 -~ DENSITY OF FLUID OVER MANOMETER FLUID. LB/FT CU
DATA CARD 5 -- INLET COEFFICIENT

DATA CARD 6 -- MANOMETER DIFFERENTIAL. IN.

DATA CARD 7 -- 4! ZERO (MA)

DATA CARD 8 -- 41 (MA)

DATA CARD 9 -- CHANGE IN VELOCITY BETWEEN POINTS CONSIDERED

DATA CARD IO - NUMBER OF POINTS CONSIDERED
VALUES FOR THE ABOVE ARE TO BE PUNCHED. WITH DECIMAL
POINT. IN THE FIRST TEN COLUMNS ON RESPECTIVE DATA CARDS.

READ ZOO.G.RO.GM.GF.CPT.H.FIZRO.FI.CV.PN

V=CPT*SQRT(2.*G*(GM-6F)/R0*H/12.)*60.

B=¢FIZRO/4.)**2

SRV=SGRT(V)

F=(FI/4.)**2

SLOPEI(F-B)/SRV

RRINT 201

PRINT 202.6.R0.GM.GF.CPT.H.V.B.F.SRV.SLOPE

NIPN

V300

RRINT 203

Do 100 1:1.N

SRVasaRTtv)

CSQISLOPE*SRV+B

CURsSORTICSO)

PRINT 2049V95RV9CSQOCUR

v=v+cv

E0RMATIFIO.0)

FORMAT(*1*)

E0RMATIE20.6* ACCELERATION DUE TO GRAVITY*/
EZO.6* DENSITY 0F ELowING FLUID*/
EZO.6* DENSITY OF MANOMETER FLUID*/
E20.6* DENSITY OF FLUID OVER MANOMETER FLUID*/
E20.6* INLET COEFFICIENT*/
EZO.6* MANOMETER DIFFERENTIAL*/
EZO.6* v AT 41*/
EZO.6* CURRENT SOUARED INTERCEPTi/
E20.6* OTHER CURRENT VALUE SOUARED*/
EEO.6* SORTIVI FOR OTHER CURRENT VALUE*/
EZO.6* SLOPE OF CALIBRATION CURVE*7(/))

203 FORMATIDX.*V(FRM)*.ax.*SORTIVI*.9x.*I~SO*.11x.*t<MA)*./)
204 F0RMAT¢4E15.3>

END

63

A.4. Program TURB

Program TURB was written for the purpose of obtaining a mean velocity,

a velocity variance, a turbulent intensity and a dispersion factor for each
"data set". This information is printed and punched out for further computer
analysis by more specialized programs. In addition to the above, program

TURB has a feature programmed in that will result in a plot of voltage fluctua-
tions, delta i,instantaneous velocity and correlation coefficients for each
data set.

The input data, order and the control cards required for program TURB are
explained at the beginning of the program listing. Interpretation of this is
as follows:

1. The parameter card controls the plotting, punching of results and
the percent of the correlation curve that is to be used when
determining the dispersion factor. If the full area is desired,

a 100 would be used. Thiszarameter card remains in effect, until
a "data set" is encountered which is followed by a blank control
card. If more data is to follow, then a new parameter card is
required.

2. The location and flow message card is used as a means of identi-
fying each "data set". The row, column and layer positiOn indica—
tor are integers, right justified in their respective fields. The
"message" allows for further identification, i.e. flow component.

3. Calibration and data constants are numbers with a decimal point and
can be positioned any place in their respective fields.

4. A value of zero in the "data set" indicates the end of the set. Be

sure to chose a reference, when recording raw data, that will produce

Three

64

only positive numbers. If the number of points in the set is a
multiple of 14, a blank card will have to be added to produce the
required "control zero". Otherwise one is not to be added. Do not
confuse this blank card with card N + 1.

error checks have been programmed in. They are as follows:

If more than 3000 data points are read in for a given "data set"
only the first 2999 and the last one are considered. A message to

this effect is printed out.
21E
IE.
1s
zero as the square root of it is to be taken. If the value is less

 

A test of the expression 1 + is made to see if it is less than
than zero it is replaced by zero and a message is printed out.

When using the wire calibration curve to convert from current to
velocity it is necessary to check the current to see if it is equal
to or greater than the current at zero velocity. If the value of
current is less than the current at zero velocity, then a print out
of the data point, the square of the current being converted, the
value of the square of the current for zero velocity and the mean

current squared is produced.

Program TURB has two subprograms which are described below.

00000000000000000000000000000000000000000000000000

PROGRAM TURB

65

ARRANGEMENT OF DATA

CARD 1. PARAMETER CARD

COLUMN

Ul-DUNH

C

00000

ODE MEANING

OR I l-IA GRAPH OF EIF IS PRODUCED

OR 1 1-A GRAPH OF DELTA I IS PRODECED

OR I 1--A GRAPH OF VELOCITY IS PRODUCED

OR I I-~A GRAPH OF CORRELATION IS PRODUCED
OR I l-RESULTS ARE PUNCHED OUT

PERCENT OF CORRELATION CURVE TO
CONSIDER FOR DISPERSION FACTOR

CARD 2. LOCATION AND MESSAGE

COLUMNS

I-S

6-10
11-15
20-59

INFORMATION

THE ROW POSITION (INTEGER)
THE COLUMN POSITION (INTEGER)
THE LAYER POSITION (INTEGER)
MESSAGE

CARD 3. CALIBRATION AND DATA CONSTANTS

COLUMNS

I~IO
11-20
21-30
31-40
41-50
51-60
61-70
71-80

INFORMATION

SQUARE UAVE VOLTAGE.EIS

NULL READING

TOTAL TIME TO RECORD SET OF DATA
VOLTAGE AMPLIFICATION FACTOR
MEAN CURRENT (4I)

RESISTANCE RATIO USED. IOED 103
SLOPE OF CALIBRATION CURVE
CURRENT SQUARED AT ZERO VELOCITY

ALL OF THE ABOVE ARE NUMBERS WITH DECIMAL

CARDS A-N.

THESE CARDS CONTAIN THE TURBLENT DATA ARRANGED IN 14 FIELDS

OF 5 COLUMNS EACH. IF THE LAST DATA CARD CONTAINS I4 SETS

OF NUMBERS.

SET OF DATA

THEN THE NTH CARD IS TO BE A BLANK CARD.
LIMIT OF 3000 POINTS HAS BEEN SET.

ALL DATA POINTS ARE GREATER THAN ZERO.

SET REFERENCE SO THAT

0(1F)0(W()0(1()0(1()0(3()0(1()0(3()0(30

100

101

102

103

104

105

106

66

CARD N+I. SAME AS CARD 2

REPEAT THE ABOVE CARDS UNTIL ALL DATA FOR A GIVEN COMPONENT
HAS BEEN CONSIDERED. THEN INSERT A BLANK CARD. IF THERE IS
ANOTHER COMPONENT TO CONSIDER. REPEAT THE ABOVE STARTING AT
CARD 1. THIS MAY BE REPEATED FOR ANY NUMBER OF COMPONENTS.

MEANING OF LETTER CODES USED IN OUTPUT

CODE MEANING

ROW POSITION IN WHICH SAMPLE WAS TAKEN
COLUMN POSITION IN WHICH SAMPLE WAS TAKEN
LAYER POSITION IN WHICH SAMPLE WAS TAKEN
MEAN OF VELOCITIES

VARIANCE OF VELOCITIES

TURBULENT INTENSITY

DISPERSION FACTOR

O0ED>7§LH

DIMENSION STOREII4)
COMMON/I/RI(500.4).SGISOOO).STG(3000.2).CISOOOIOMR(500.3)
COMMON‘N.CT.ICOFF.NP

READ 200.NEIF.NDI.NV1.NCP.NPUNCH.ICOFF
IF(EOF960)127.IOI

DO 102 J8194

DO 102 181.500

RIIIQJI'OD

NPBO

NP=NP+I

READ 201.MR(NP.I).MR(NP.2).MR(NP.3).WA.WB.WC.WD.WE
IF(MR(NPQI)OEQOO, GO TO 123

N30

READ 202.EISOB.TF9VAF9AC4T9RER.SL.YIC
ACPAC4T/4o

ACSQD=AC*AC

READ 203.($TORE(I).I=1.14)

DO 105 181.14

IFCSTORE(I).EQ.O.) GO TO 106

N=N+1

IF(N.LE.3000) GO TO 105

N=3000

IFLAG’I

GO TO 104

SG(N)‘STORE(I)

GO TO 104

CT=TF/(N~I)

T‘O.

67

DO 107 I=1.N
STGII.I)=T

107 T3T+CT
PRINT 2040MRINPQI).MRINpoa).MRINPOBICWAGWBOWCQWDOWE
IFIIFLAGDEGOI) PRINT 205
PRINT 206.AC.N.CT.B.RER.VAF.EIS
PRINT 207.ISG(11.1*10N)
SUMBOO
Do 108 1310N

108 SUMSSUM+SGIII
O'N
YBSSUM/O
DO 109 I=1.N

109 SGII)=SG(I)-YB
DO 110 1310N

110 SGIII=$GII)*VAF
IFINEIFONE01) GO TO 112
DO 111 1319N

111 STGIIOZIPSGII)
PRINT 208
CALL GRAPH

112 $183.05/IIO+B*RER/4OOO)
BGG'OO
SMM31000E+300
DO 115 I=1.N
TBR810+2.*SI/AC*SG(II/EIS
IFITBROLTOSM") SMMITBR
IFITBR.GT.BGG) BGGITBR
IFITBROLT0011130114

113 SGIII=00
PRINT 2090MR1NP01)QMRINP.2).MR(NP.3)OI
GO TO 115

I14 SGII)‘AC*(SORTITBR)“10)

115 CONTINUE
IF(NDIONE01) GO TO 117
DO 116 I=I.N

116 5T61102135611)
PRINT 210
CALL GRAPH

117 BODBACSOD
DO 118 I‘loN
DDBIAC+$GII))**2
IF(DDOLT.BDD) BOD'DD
IFIDDOLTOYIC) PRINT 2159IODDOYICOACSGD

118 SGII)‘((DD-YIC)/SL)**2
IFINVIONEOII GO TO 120
DO 119 I=ION

119 STG1192135GII)
PRINT 211
CALL GRAPH

120 CALL STAT
IFINCPONEOI) GO TO 122
DO 121 I=ION

121 STGIIO213CII)
PRINT 212
CALL GRAPH

122

123

I24

I27
200
201
202
203
204
205

206 FORMAT(5X.F15.5.*

207
208
209
210
211
212
213
214

C

000000

000000000

68

PRINT 213 I

PRINT ZIAOIRIIvaK).KaI.4)OSI.SMMvBGGQACSODQYICOBDD

GO TO 103

NPRNP‘I

PRINT 216

DC 124 I=1.NP

IFINPUNCHOEQOOI GO TO 124 ,

PUNCH ZITOIMRIIOJ)9J=1.3).(R1(I.J)9J=l.4)

PRINT 2180(MR(I.J).J=I.3).(R1(I.J)9J21.4)

IFINPUNCHoEQeO) GO TO 100

PUNCH 219

GO TO 100

CONTINUE

FORMAT1511913)

FORMATI31504X95A8)

FORMATIBFIOOZI

FORNATIIAFSOII

FORMAT(*1*.*ROW*I39* COLUMN*0I39* LAYER*.I3.5X95A8.2(/))
FORMAT122X.*NORE THAN 3000 DATA POINTS WERE ENTERED. ONLY THE FIR
ST 2000 WERE CONSIDERED*.2(/I)

OPERATING CURRENT. MA.*/

5X.II5 .* NUMBER OF DATA POINTS PER GRAPH*/
5X.F15.5.* TIME INTERVAL BETWEEN POINTS. SEC.*/
5X9F15.5.* NULL READING*/

5X.FI5.5.* OPERATING RESISTANCE RATIO. OHMS*/
5X.F15.5.* VOLTAGE AMPLIFICATION FACTOR*/
5X9F15.5.* SQUARE WAVE VOLTAGE. VOLTS*.3(/))

FORMATIIX.15F9.3)

FORMAT(*1*.IOX.*PLOT OF EIF*.2(/))

FORMATIIOX.415.* NEGATIVE*)

FORMAT(*1*.IOX.*PLOT OF DELTA I*.2(/))
FORMAT(*1*.10X.*PLOT OF V(T) -- FEET PER MIN*.2(/))
FORMAT(*1*.IOX.*PLOT OF CORRELATION*.2(/))

FORMAT(*-*)

FORMAT(5X.F15.5.* MEAN OF VELOCITY*/
5X.F15.5.* VARIANCE OF VELOCITY*/
5X.F15.5.* INTENSITY OF TURBLENCE*/
5X.F15.5.* DISPERSION FACTOR*/
5X.F15.5.* SQUARE WAVE CURRENT*/

5X.F15.5.27H SMALL l.+2.*SI/AC*EIF/EIS./
5X.F15.5.27H LARGE I.+2.*SI/AC*EIF/EIS./

5X.F15.5.* MEAN CURRENT SQUARED*/
5X.Fl5.5.* ZERO VELOCITY CURRENT SQUARED*/
5X.F15.5.* SMALLEST CURRENT SQUARED*)

215 FORMAT(*-*.12X.*ERROR*.IIOO3F15.5)

215 FORMAT(*1*.3x,*1*,3x.eJ*,3x.*K*.64H ****** A ****** ****** a ***I*
C* *ifliii c ****** ****** D ******./)

217 FORMAT(1X.313.4F15.5)

218 FORMATIIX.314.4F16.5)

219 FORMATI* *)

6
A.4.a. Subprogram STAT 9

Subprogram STAT contains the equations that produce the mean velocity,
velocity variance, turbulent intensity and dispersion factor for a "data

set" when called.

SUBROUTINE STAT
COMMON/I/RII5OOQ4)95G(3000).STGI300002).C(3000)9MR(500.3)
COMMON N.CT.ICOFF.NP
SUM=OO
DO 100 I'IoN
100 SUM=SUM+SGIII
BRN
YB=SUM/B
SUM=Oe
DO 101 1310N
101 SUM:SUM+(SG(I)—YB)**2
VAR=$UM/B
SDBSORTIVAR)
T1=SD/YB
R1(NP.1)=YB
R1(NP.2)=VAR
R1(NP.3)=TI
K=N
L30
1030
BETASIO
IFITIoLTOOOOOOOI) GO TO 102
BETA=SORTI3O141592)/(4.*TI1
102 SUMSOO
DO 103 I=10K
M=I+L
103 SUM=$UM+ISG(I)‘YB)*(SG(M)-YB)
KBK-1
L3L+1
IC=IC+1
C(ICIPSUM/VAR/B
IFIKOGE01)102.104
104 CONTINUE
SUM=Oo
NH=(N*ICOFF)/IOO
DO 105 1:2.NH
105 SUM=SUM+ABSIC(I‘1)+C(1))/2.*CT
R1(NP94)=VAR*SUM*BETA/60.
END

70

A.4.b. Subprogram GRAPH

Subprogram GRAPH was written for the purpose of obtaining a visual

representation of the data, if desired.

100

102

103

104
200
201

SUBROUTINE GRAPH

DIMENSION KPIIOI)
COMMON/1/R1‘5OOO4)05G13000105TGI3O0002)OCISOOO).MR150093)
COMMON‘N.CT.ICOFF.NP
DATAIKM=1H“)9(KI=1HI)OIKH=IH*)
8:-IOOOE+300

53+IOOOE+3OO

DO 100 I=1.N

IFISTGIIQ210LTOS) 585TG1102)
IFISTGIIO2).GTOBI B=STG11921

CONTINUE

STEP=(B‘S)*.OI

S$=*S

IC=1

IFISOLTOOD) IC=-S/STEP+1.5

DO 102 1:29100

KPIII=KM

KPIII=KI $ KPIIC1=KI $ KPIIO1)=KI
PRINT ZOOCIKPIIIOI=191011

DO 104 I=1.N

DO 103 J=10101

KPIJ1=8H

KPIII=KI 5 KPIICIBKI $ KP110113K1
IL=ISTGI1921+SSI/STEP+1.5

KPIIL1=KH

PRINT ZOIOSTGIIOII.STG(IQ2).(KP(K)9K=I9101)
FORMAT(* *96X.*X*013XO*F(X)*08X9IOIAI)
FORMATI1X0E120592X9E1508.3X0IOIAI1

END

71

1

 

Sample of Input Data

A.4.c.

H0
N0 "0 ~0 00 00 N6 00 00 00 00 06 F6
~0 00 00 00 06 N0 00 06 00 06 00 00
60 06 60 00 06 00 00 00 00 06 00 00
F0 00 06 06 F0 F6 00 N0 #6 00 00 06
00 00 N0 0K 00 N0 00 00 b6 06 A0 00
00 06 66 F6 00 ~0 60 00 00 N0 00 00
00 00 00 N0 «0 N6 00 F0 F6 00 00 06

00.0NHO 00.00“ 00.~ 00.000 00.H 00.0 00.00
BOJL J<U~kam> a

0.0 0.0 0.6 0.6 0.0 0.F 6.6 0.b 0.0 0.0 6.6

0.6 0.0 0.h 0.0 6.N 6.0 0.0 6.b 0.0 0.0 0.0

h.6 N.0 ".0 N.0 0.6 N.b 0.0 0.0 0.0 0.0 0.6

0.F Ooh N.0 0.0 0.0 0.0 0.0 0.F 0.0 6.0 0.0

0.6 0.6 0.F 0.0 0.0 ".0 F.0 0.0 0.5 N.0 0.0

0.0 0.0 0.0 0.0 —.0 0.0 N.0 0.0 N.0 0.0 0.6

6.—~ F.0 0.0 F.F 0.6 0.6 0.P 0.0 0.0 0.F 0.6

00.0NHO 00.0N~ 00.— 00.660 00." 00.0 00.00
3040 thZONHEOI w

0000.00
KINlnP‘m\OF‘0
0.0000
00.00..
WCFGIOIDUTUIP

OON¢NN~O
001006001016
I‘VUIO‘IOI‘I‘ID
I‘OOO‘I‘O‘NO

0
0
(U0.

0‘.
H

O
In
H

000000

72

A.5. Program ANALl

100

101
102

103

106

107

108

109

The functions of program ANALl are explained in section 4.3.2.

PROGRAM ANALI

DATA CARDS I TO 253. PUNCHED DATA AS RECEIVED FROM PROGRAM
TURB. 126 CARDS'FOR EACH COMPONENT. SEPARATED BY A
BLANK CARD.

DATA CARDS 254 TO N. COLUMNS OF ARRAY D TO BE PAIRED.

COMMON/1/DI200913)
COMMON/Z/ARM(20.20).NZ.BR(2091).MTS.DET
DIMENSION L(51.101).Z(51)9NR(7.101).ML(IOI)
DATAIKM=IH*).(KB=1H ).(KI=1HI).(KS=1H*).(KP=1H.).(KPS=1H+)
N=126

NP18N+1

DO 100 181.NP1

READ 300.‘D(I.J).J=I.7)

PRINT 203

DO 101 I=1.N

READ 302.(D(I.J).J88911)
DIIOIZISSORTIDII.4)*D(Iv4)+D(I.B)*D(IQB))
DI1.1318ATAN(D(108)/D(1.4))*57.296
PRINT 3039(DIIOJ).J=1.13)

READ 201.1X.IY

IFIEOF.60)1259103

BX=D(1.IX)

DO 106 I=1.N

IFIDII.IX).GT.BX) BX=D(I.IX)

CONTINUE

SX=BX*0.01

DO 107 131.101

AI=I-1

NX=SX*AI*10000.

DO 107 J=197

K=NX-(NX/10)*IO

NRCJ.I)3K

NXBNX/IO

BY=D(1.IY)

DO 108 I=1.N

IFIDIICIY).GT.BY) BY=D(I.IY)

CONTINUE

SYBBY*0.02

ZISIIFOO

DO 109 131.50

AI=I

ZI51~I1=SY*AI

114

115
116

73

DO 110 I=1.51

DO 110 J=1.101
L(I.J)3KB

DO 111 I=1.N
IRR=D(I.IY)/SY+O.5
IR=51-IRR
JC=D(I.IX)/SX+I.5
L(IR.JC)=KM

X=O. s Y=0. S XY=0. $ X2=O.
02:0. S 03:0. S Y2=O.
DO 112 I=1.N

DX=D(I.IX)

DY=D(I.IY)

05=DY*DY

D6=DX*DY

D7=DX*DX

D8=D6*DX

D9=DT*DX

DIO=D9*DX

X=X+DX

Y=Y+DY

XY=XY+D6

X2=X2+DT

Y2=Y2+D5

X2Y=X2Y+DB

X3=X3+D9

X4=X4+DIO

CONTINUE

AN=N

Q=AN*X2-X*X
A=(X2*Y~X*XY)/O
B=(AN*XY-X*Y)/Q

DO 113 I=1.N
YC=A+B*D(I.IX)
D2=D2+(D(I.IY)-YC)**2
SY=SQRT(D2/AN)
ZY=SQRTIY2/AN-(Y/AN)**2)
COC=SORT(1-SY*SY/(ZY*ZY))
PRINT 200.1X.IY

PRINT 209.A.B.SY.COC

DO 116 J=1.101
IF(NR(7.J).EQ.0)114.116
NR(7.J)=BH
IF(NR(6.J).EQ.O)115.116
NR(6.J)=BH

CONTINUE

BR(1.1)=Y

BR(2.I)=XY

BR(3.1)=X2Y

S

X2Y=Oe

$

X3=00

S

X4300

74
ARM(1.I)=AN
ARM¢1.2)=X
ARM(1.3)=X2
ARM(2.1)=X
ARM(2.2)=X2
ARM(2.3)=X3
ARM(3.1)=X2
ARM(3.2)=X3
ARMI3.3)=X4
NZ=3
MTS=1
CALL MATINV
A=BR(1.1)
B=BR(2.1)
C=BR(3.1)
DO 117 1=1.N
YC=A+B*D(I.IX)+C*D(I.IX)*D(I.IX)
117 D3=D3+(D(I.IY)-YC)**2
SY=SQRT(D3/AN)
RHO=SQRT(1~SY*SY/(ZY*ZY))
PRINT 210.A.B.C.SY.RHO
119 PRINT 203
DO 120 I=1.51
120 PRINT 202.Z(I).KI.(L(I.J).J=1.101).KI
DO 121 1:1.101
121 ML(I)=KS
PRINT 205.KI.(ML(I).I=1.101).KI
DO 122 1:1.4
122 PRINT 206.(NR(1.J).J=1.101)
DO 123 I=1.IOI
123 ML(I)=KP
PRINT 211.(ML(I).I=I.101)
DO 124 I=5.7
124 PRINT 206.(NR(I.J).J=1.IOI)
GO TO 102
I25 CONTINUE
200 FORMAT(*1*.4X.*COLUMNS*.I3.* AND*.I3.* OF THE ABOVE WERE USED*)
201 FORMAT(212)
202 FORMAT(FIO.4.1X.IO3A1)
203 FORMAT(*I*)
205 FORMATIIIX.103A1)
206 FORMATIIZX.101R1)
209 FORMAT(*O*.IOX.*Y = A + B X*// 6X.*WHERE A=*.El7.9.//.I4X.

C *B=*.E17.9.//.
C 11X.*THE STANDARD ERROR OF ESTIMATE IS*.E17.9//‘
C 11X.*THE COEFFICIENT 0F CORRELATION IS*.E17.9)
210 FORMAT(*O*QIOX.*Y = A + B X + C X X*//6X9*WHERE A=*.EI7.9o//0
C 14X.*B=*.E17.9.//.14X.*C=*.E17.9.//.
C 11X.*THE STANDARD ERROR OF ESTIMATE IS*9E17.9//
C 11X.*THE INDEX OF CORRELATION 15*951709)

211 FORMAT(12X.101A1)

300 FORMAT(IX.313.4F15.5)

302 FORMATIIOX.4F15.5)

303 FORMAT(3X.3I3.IOF12.5)
END

0()0 0(7C)0

C)0(T

A.5.a. Subprogram MATINV 75

MATINV was obtained from the Computer Library at Michigan State

University. The CO-OP identification is Fl NBSB MATINV. Its title is

"Matrix Inversion with Accompanying Solution of Linear Equations", written

by Burton S. Garbow.

MATINV was used to determine the solution of the linear equation

produced by program ANALl.

10
15
20
30

4O
45
50
6O
70
80
85
90
95
100
105
110

130
140
150

SUBROUTINE MATINV

F1 NBSB MATINV MATRIX INVERSION
MATRIX INVERSION WITH ACCOMPANYING SOLUTION OF LINEAR EQUATIONS

COMMON/2/A(20.20).N.B(20.1).M.DETERM
DIMENSION IPIVOT(20).INDEX(20.2).PIVOT(20)

INITIALIZATION

DETERM31 e O
D0 20 J=I.N
1P1VOT(J)=O
DO 550 I=1.N

SEARCH FOR PIVOT ELEMENT

AMAX=OOO

DO 105 J=19N

IF (IPIVOTIJ1‘1) 600 105. 60
DO 100 K=10N

IF (IPIVOTIK)-1) BO. 100. 740

IF (ABSFIAMAX)-ABSF(A(J.K))) 85. 100. 100
IROW=J

ICOLUM=K

AMAX=A(J.K)

CONTINUE

CONTINUE

IPIVOTIICOLUM)=IPIVOT(ICOLUM)+I
INTERCHANGE ROWS TO PUT PIVOT ELEMENT ON DIAGONAL
IF (IROW-ICOLUM) 140. 260. 140
DETERMI-DETERM

DO 200 L=I.N

0(30

0(30

0(30

160
I70
200
205
210
220
230
250
260
270
310
320

330
340
350
355
360
370

380
390
400
420
430
450
455
460
500
550

600
610
620
630
640
650
660
670
700
705
710
740
750

76

SWAP=A(IROW.L)
AIIROW.L)=A(ICOLUM.L1
AIICOLUMQLIPSWAP

IF(M) 260. 260. 210
00 250 L=l. M
SWAP=BIIROW9LI
BIIROW.L)=B(ICOLUM.L)
B‘ICOLUMQL)=SWAP
INDEX(I.1)=IROW
INDEXIIO21=ICOLUM
PIVOTII)=A(ICOLUM.ICOLUM)
DETERM=DETERM*PIVOT(I)

DIVIDE PIVOT ROW BY PIVOT ELEMENT

A(ICOLUM.ICOLUM)=1.0

DO 350 L=1.N
AIICOLUM.L)=A(ICOLUM.L)/PIVOT(I)
IF(M) 380. 380. 360

D0 370 L=1.M
B(ICOLUM.L)=B(ICOLUM.L)/PIVOT(I)

REDUCE NON-PIVOT ROWS

DO 550 L1=I.N

IF(LI‘ICOLUM) 400. 550. 400
T=AIL101COLUM)
A(L1.ICOLUM)=0.0

DO 450 L=19N
A(L1.L)3A(L1.L)-A(ICOLUM.L)*T
IF(M) 5509 550. 460

D0 500 L=1.M
BILIOLI=B(L10L)‘B(ICOLUM.L)*T
CONTINUE

INTERCHANGE COLUMNS

DO 710 I=1.N

L=N+1~I

IF (INDEXIL.1)‘INDEX(L.2)) 630. 710. 630
JROW=INDEX(L91)
JCOLUM=INDEX(L.2)

DO 705 K=1.N
SWAP=A(K.JROW)
AIK.JROW)=A(K.JCOLUM)
AIK.JCOLUM)=SWAP
CONTINUE

CONTINUE

RETURN

END

()0(1()0(1

77

A.6. Program ANAL2

100

101

104

105

106

107

108

The function of program ANAL2 is explained in section 4.3.b.

PROGRAM ANAL2

DATA CARDS 1 TO 253. PUNCHED DATA AS RECEIVED FROM PROGRAM
TURB. 126 CARDS FOR EACH COMPONENT. SEPARATED BY A
BLANK CARD.

DATA CARDS 254 TO N. COLUMN OF ARRAY D TO BE USED.

COMMON/1/DI200013)

DIMENSION IM(6)OIW(IOO).STG(IOO)
DATAIIM=1H-.1HT.1HL.1HH.1H=.1H )
N=126

NPI=N+1

DO 100 I=1.NP1

READ 200.(D(I.J).J=1.7)

PRINT 208

00 101 I=1.N

READ 201.‘D(1.J).J=B.11)
DII.12)=SORT(D(I.4)*D(I.4I+D(1981*011981)
DII.13)=ATAN(D(I.B)/D(I.4))*57.296
PRINT 202.(D(I.J).J=1913)

NIW=18

READ 207.ISET

IF(EOF.60)113.105

PRINT 2OBQISET

DO 111 1231.2

SM=+1.00E+300

BG=-I.00E+300

DO 106 I=I.N

IF(DIIOISET).EQ.O.) GO TO 106
IF(DII.ISET).LT.SM) SM=D(I.ISET)
IF(DIIOISET).GT.BG) BG=D(I.ISET)
CONTINUE

STEP=(BG-SM)/5.

PRINT 204

1F=0

K=O

DO 108 I=I.NIW

K=K+1

IF(K.EO.N) IFSI

STG(II=D(K.I$ET)

DO 110 I=195

78

1J=I-1
Do 109 J=1.NIW
IwIJI=IM<OI
1F(STG(J).GE.SM+STEP*IJ) IWIJ)=IM¢I)
109 CONTINUE
110 PRINT 205.(1W(JJ).JJ=1.NIW)
RRINT 206
IF(IF.NE.I) GO To 107
PRINT 204
Do 111 I=1.N
IF(DII.ISETI.OT.STER) D(I.ISET)=O.
111 CONTINUE
GO To 104
113 CONTINUE
200 FORMAT(1X.313.4F15.5)
201 FORMATIon.4FIs.5)
202 FORMAT(3X.313.10F12.5)
203 FORMAthIIOI
204 FORMAT(*-*)
205 FORMAT(*+*.10X.IOOA1)
206 FORMAT(* *)
207 FORMATIIeI
208 FORMAT(*1*.4X.*COLUMN*.13.* OF THE ABOVE WAS USED*2(/))
END

79

A.7. Program TURB Output

For each

I

of the two tabulations the following key will be used:
row position in which sample was taken
column position in which sample was taken
layer position in which sample was taken
mean velocities (FPM)

variance of mean velocities

turbulent intensity

dispersion factor

80

A.7.a. Horizontal Component

H

UUUUUUUUUNNNNNNNNNNNNNNNNNNHHH-H~HH~H“H“HHHH

J K A B C D
1 1 103.16799 2865.61671 0.51888 7.76830
2 1 81.38393 1318.69226 0.44620 6.55796
3 1 105.73176 1264.52801 0.33632 7.51664
4 1 69.09943 782.76204 0.40489 2.66035
5 1 84.56966 314.40131 0.20967 2.36208
6 1 57.77905 324.69438 0.31187 3.58720
7 1 47.91953 157.69940 0.26206 1.02215
8 1 47.89539 152.87151 0.25815 0.92225
9 1 39.46102 127.80799 0.28649 0.96937
10 1 43.21369 75.13250 0.20058 0.56877
11 1 13.76886 10.35076 0.23366 0.07909
12 1 21.58245 13.21400 0.16843 0.10720
13 1 38.88841 28.95535 0.13837 0.44699
14 1 4.61190 1.09328 0.22672 0.00680
15 1 2.33742 0.27517 0.22442 0.00199
16 1 21.45046 1.38033 0.05477 0.04563
17 1 13.59832 0.45352 0.04952 0.01988
18 1 0.36946 0.00583 0.20664 0.00006
1 1 0.09242 0.00046 0.23263 0.00000
2 1 1.59814 0.75546 0.54386 0.00149
3 1 23.03937 148.16834 0.52833 0.50105
4 1 22.76979 110.14264 0.46091 0.44088
5 1 49.81214 522.12541 0.45872 2.07107
6 I 33.26733 283.07316 0.50574 0.86896
7 1 33.20042 299.03021 0.52085 1.19944
8 1 32.38358 165.93026 0.39778 0.68546
9 1 32.31534 157.70653 0.38861 0.79400
10 1 32.27799 147.80006 0.37664 0.736OO
11 1 31.52786 48.70920 0.22137 0.33868
12 1 31.27795 15.88211 0.12741 0.24003
13 1 31.61639 63.19010 0.25143 0.33491
14 1 13.68789 5.47917 0.17101 0.04565
15 1 13.70143 5.75899 0.17515 0.06639
16 1 18.70706 6.94874 0.14091 0.10638
17 1 1.47700 0.02815 0.11360 0.00036
18 1 13.65626 3.73322 0.14148 0.03821
1 1 0.09116 0.00000 0.00000 0.00000
2 1 1.47287 0.00278 0.03578 0.00009
3 1 4.55221 0.00000 0.00000 0.00000
4 1 4.55231 0.00185 0.00946 0.00025
5 1 3.35131 0.21745 0.13914 0.00270
6 1 13.67968 5.13755 0.16569 0.04345
7 1 11.71780 14.89947 0.32941 0.10284
8 1 19.17067 37.94895 0.32134 0.24066
9 1 35.66828 133.43355 0.32385 0.83819

UIUIU'IU'IUIUIUIU'IU'IUIUIUIUIUIUIUIUIUIDbDhbbbbhbbbbbbbbbUUUUUUUUU

HI‘HHHHI—DH
QO‘UIéUN-‘O

DI.
\DCDQOUIhUNHm

\OOQO‘WDUN”

a
0

ll

13
14
15
16
17
18

[JHHHHHHflHHflfi-IH

HHHHHMF‘O‘HHHHD‘HHHHHflfi-‘HHHHHHHHHHHH

32.10888
24.97369
35.20492
21.54057
24.58980
24.50881
3.35194
5.98479
9.40898
2.30815
5.96522
7.57267
2.30807
2.30324
2.30796
2.30929
4.55444
5.96774
4.57825
5.98331
4.57999
9.43739
9.44160
4.62494
13.60069
27.71255
27.71497
1.47250
0.82571
1.47248
3.33401
2.30800
2.30815
2.30899
4.55314
7.57318
2.30915
4.55246
3.33756
4.55800
4.55414
2.31841
1.47698
9.37939
9.37995

81

124.14436
50.27442
53.05541

9.06827

12.56912

4.60498
0.25229
0.48562
1.11922
0.00213
0.01660
0.00000
0.00138
0.00299
0.00041
0.01236
0.03988
0.07401
0.47786
0.44321
0.49117
2.15975
2.26173
1.31321
0.59162
1.00784
1.27510
0.00062
0.00034
0.00048
0.00108
0.00078
0.00213
0.00980
0.01722
0.01540
0.01149
0.00469
0.04849
0.10801
0.03536
0.09471
0.02689
0.03596
0.05670

0.34701
0.28392
0.20690
0.13980
0.14418
0.08756
0.14985
0.11644
0.11244
0.02000
0.02160
0.00000
0.01608
0.02368
0.00878
0.04814
0.04385
0.04559
0.15099
0.11127
0.15302
0.15572
0.15928
0.24778
0.05655
0.03623
0.04074
0.01696
0.02226
0.01488
0.00987
0.01213
0.02000
0.04287
0.02832
0.01638
0.04642
0.01504
0.06598
0.07210
0.04129
0.13274
0.11102
0.02022
0.02539

0.77291
0.25971
0.47919
0.11318
0.12262
0.08444
0.00362

'0.00646

0.02437
0.00010
0.00082
0.00000
0.00030
0.00019
0.00008
0.00040
0.00183
0.00197
0.00598
0.00946
0.00588
0.02057
0.02205
0.01056
0.01941
0.04701
0.05811
0.00005
0.00003
0.00006
0.00020
0.00007
0.00018
0.00058
0.00097
0.00168
0.00047
0.00085
0.00163
0.00199
0.00201
0.00087
0.00029
0.00324
0.00435

~JQ~J‘J4-4~44-4~J4-4~Jfl-4~14-40\0(30\0(fi0‘0(fi0‘0(fi0‘0(10‘0(h

©tn~40\m.bcan)~

fiHwflHHHwflHHnanny-.Hpag—Apdh.flflpHHr‘HHHHHflHfiug—A

3.33393
2.30797
1.47240
0.09138
4.55226

13.59014

2.30818
9.37925
4.55399
7.57477
3.34265
0.83661
2.30815
3.33424
1.47325
5.96899
2.30833
1.47266
2.30792
3.33393
1.47240
0.36578
0.82561
1.47269
7.57316

18.61395
16.00132
13.60836

2.31419
4.55379
3.33501
5.96501
0.36687
4.55237
4.55567
4.55396

82

0.00000
0.00045
0.00000
0.00008
0.00091
0.00811
0.00245
0.03070
0.03172
0.06288
0.11679
0.03572
0.00217
0.00417
0.00501
0.10619
0.00389
0.00153
0.00000
0.00000
0.00000
0.00000
0.00000
0.00172
0.01481
0.02608
0.12435
1.00308
0.05979
0.02880
0.01435
0.01151
0.00165
0.00294
0.06236
0.03136

0.00000
0.00918
0.00000
0.09991
0.00662
0.00663
0.02142
0.01868
0.03911
0.03310
0.10224
0.22590
0.02018
0.01936
0.04805
0.05459
0.02700
0.02657
0.00000
0.00000
0.00000
0.00000
0.00000
0.02820
0.01607
0.00868
0.02204
0.07360
0.10566
0.03727
0.03592
0.01799
0.11068
0.01190
0.05481
0.03889

0.00000
0.00008
0.00000
0.00000
0.00035
0.00241
0.00022
0.00242
0.00145
0.00325
0.00220
0.00036
0.00026
0.00036
0.00018
0.00412
0.00023
0.00015
0.00000
0.00000
0.00000
0.00000
0.00000
0.00013
0.00180
0.00237
0.01510
0.03270
0.00087
0.00157
0.00072
0.00184
0.00004
0.00055
0.00205
0.00179

H

UUUUUUUUUNWNNNNNNNNNNNNNNNNflv-‘Ht‘Hr-er-Hr-Ht-Hv-HHu-

A.7.b.

L4

OID~JO‘m.bCJhDH

0(DsJOLfibWJh)»

W

HflflHHHflg-DHflflHHflHflHHHflHflflp‘flflO-OHflflflHHHwflHHHHflHHHfi

Vertical Comgonent

A

28.50664
28.28282
22.03529
13.84533
13.90525
11.43297
11.47599
11.45011
11.44509
11.45582
9.40686
7.59383
1.47500
5.97182
1.48956
1.47280
4.55265
5.97081
0.36614
0.37707
4.61015
5.99411
9.73475
9.50255
13.93578
11.60246
13.64184
16.03217
16.02910
16.04862
11.39649
7.58044
2.31504
3.33568
9.38686
5.96651
0.09116
0.82561
0.82561
0.82568
0.82761
0.83310
2.37969
2.31233
2.32124

83

B

91.24353
62.34143
49.56181
13.15841
16.35394
2.19728
4.22947
3.00362
2.80231
3.19941
1.02929
0.61265
0.01503
0.17207
0.11138
0.00234
0.00809
0.15120
0.00054
0.01586
0.97744
0.71348
13.50344
4.54554
19.10922
7.68699
2.80282
2.02289
1.89115
3.10567
0.57208
0.22847
0.06800
0.02297
0.31287
0.04704
0.00000
0.00000
0.00000
0.00024
0.00607
0.02188
0.59699
0.03946
0.12099

C

0.33508
0.27917
0.31949
0.26200
0.29083
0.12965
0.17921
0.15136
0.14626
0.15614
0.10785
0.10307
0.08311
0.06946
0.22405
0.03285
0.01976
0.06512
0.06323
0.33399
0.21445
0.14092
0.37748
0.22436
0.31368
0.23896
0.12272
0.08871
0.08579
0.10981
0.06637
0.06306
0.11264
0.04543
0.05959
0.03635
0.00000
0.00000
0.00000
0.01892
0.09417
0.17755
0.32469
0.08590
0.14985

D

0.28082
0.35651
0.22612
0.07258
0.07662
0.02434
0.04174
0.02737
0.02162
0.03126
0.01171
0.00757
0.00030
0.00485
0.00090
0.00014
0.00071
0.01747
0.00001
0.00007
0.00591
0.00838
0.03842
0.02682
0.10298
0.04817
0.03164
0.03650
0.03778
0.03610
0.01395
0.00716
0.00301
0.00078
0.02958
0.00168
0.00000
0.00000
0.00000
0.00001
0.00010
0.00021
0.00335
0.00068
0.00116

mt”UlmLflU1WC£U1mLflUlmtflUim(301b«bJ>b-b£>¢<h£#b4bbwbl>b-DJ>D(JLJU(JUJU{JOJU

HHHl-lhfit-‘h‘h-O
4(fiUlb(Jh)H£D

pd
©<n~¢o<n¢>mru-m

hit-OHHI—Ihit-OHHHHHHHHHHHHHHHHflflHHHHflHD—lHMHHHHHHHHHHH

2.31852
4.56220
2.31109
2.31415
1.47338
0.36585
0.37004
1.49183
0.36675
0.82561
0.82561
0.36585
0.36584
0.36578
0.82573
0.82568
0.82585
0.82602
0.82785
0.82671
0.82638
0.82628
0.83718
0.82572
2.30851
2.31004
2.30868
0.09116
0.09116
0.09116
0.09123
0.09139
0.82588
0.82601
0.82580
0.82581
1.47319
1.47511
0.82636
4.55355
0.82606
2.30873
2.30968
2.30940
2.30826

84

0.09824
0.18033
0.02962
0.07462
0.00580
0.00010
0.00613
0.11414
0.00142
0.00000
0.00000
0.00011
0.00010
0.00001
0.00040
0.00025
0.00083
0.00134
0.00745
0.00366
0.00254
0.00224
0.03793
0 . 00039
0.00545
0.01852
0.00694
0.00000
0.00000
0.00000
0.00003
0.00009
0.00093
0.00134
0.00062
0.00067
0.00468
0.01644
0.00250
0.02453
0.00152
0.00763
0.01644
0.01389
0.00310

0.13519
0.09308
0.07447
0.11804
0.05170
0.02746
0.21153
0.22646
0.10262
0.00000
0.00000
0.02865
0.02702
0.00795
0.02424
0.01909
0.03478
0.04432
0.10427
0.07317
0.06104
0.05730
0.23262
0.02383
0.03198
0.05891
0.03609
0.00000
0.00000
0.00000
0.05548
0.10182
0.03695
0.04430
0.03025
0.03127
0.04645
0.08693
0.06049
0.03439
0.04716
0.03784
0.05552
0.05103
0.02413

0.00140
0.00254
0.00067
0.00049
0.00025
0.00001
0.00006
0.00077
0.00003
0.00000
0.00000
0.00001
0.00001
0.00000
0.00003
0.00003
0.00003
0.00005
0.00012
0.00018
0.00010
0.00008
0.00035
0.00003
0.00032
0.00041
0.00036
0.00000
0.00000
0.00000
0.00000
0.00000
0.00005
0.00007
0.00005
0.00005
0.00013
0.00023
0.00010
0.00107
0.00006
0.00045
0.00065
0.00044
0.00023

s14-J~J4~J~34-4~Jd-4~44-4~14~40\0(fiO‘OCfiO‘OC)O‘O()O‘O(DO\m<1

W)D~JO*m-bhlm*‘

HHHHHHHh‘Hh‘HHHHHHI—OI—dHHHHHflHflumanHmo-fino...

0.36578
0.36578

'0.09116

0.36586
0.82570
0.82569
0.82561
0.82569
0.82638
0.82561
0.82745
0.82569
0.82629
0.82601
0.82734
0.09169
3.33515
3.33527
2.30792
0.09116
0.09116
0.36585
0.36583
0.36583
0.36586
0.36586
4.55232
2.31033
3.33429
1.47273
1.47279
1.47243
1.47269
1.47242
2.30852
0.82569

85

0.00000
0.00000
0.00000
0.00011
0.00032
0.00027
0.00000
0.00029
0.00234
0.00000
0.00614
0.00029
0.00219
0.00138
0.00549
0.00018
0.01626
0.01822
0.00000
0.00000
0.00000
0.00010
0.00007
0.00007
0.00012
0.00012
0.00202
0.02352
0.00491
0.00200
0.00231
o;ooozo
0.00176
0.00010
0.00562

0.00029

0.00000
0.00000
0.00000
0.02897
0.02168
0.02004
0.00000
0.02052
0.05853
0.00000
0.09467
0.02063
0.05665
0.04489
0.08953
0.14767
0.03824
0.04047
0.00000
0.00000
0.00000
0.02727
0.02348
0.02298
0.03055
0.03019
0.00986
0.06638
0.02102
0.03035
0.03260
0.00969
0.02850
0.00667
0.03247
0.02064

0.00000
0.00000
0.00000
0.00001
0.00001
0.00002
0.00000
0.00002
0.00005
0.00000
0.00012
0.00002
0.00008
0.00004
0.00010
0.00000
0.00110
0.00059
0.00000
0.00000
0.00000
0.00002
0.00002
0.00001
0.00001
0.00001
0.00027
0.00047
0.00029
0.00012
0.00010
0.00003
0.00013
0.00001
0.00021
0.00002

REFERENCES

86

REFERENCES

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Daugherty, R. L. and Ingersoll, A. C.
1954 Fluid Mechanics with Engineering Applications. Fifth Edition.
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Eckman, Donald P.
1950 Industrial Instrumentation, John Wiley and Sons, Inc. New York.
Esmay, Merle L.
1960 Design Analysis for Poultry - House Ventilation. Agricultural
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1952 The Ventilation Air Jet. Journal of the Institution of Heating
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1953 Turbulent Diffusion: Mean concentration distribution in a flow

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Harrington, Jr., J. B.

1965 Atmospheric Pollution by Aeroallergens: Meteorological Phase.
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Henderson, S. M. and Perry, R. L.

1955 Agricultural Process Engineering, John Wiley and Sons, Inc. New

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Kunze, Otto R.

1964 §gg§r Beet Seed Research. Agricultural Engineering Laboratory

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1960 Heat and Moisture Design for Poultry Housing. Agricultural

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Olsen, Reuben M.
1961 Essentials of Engineering Fluid Mechanics. International Text—
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Pao, Richard H. F.
1961 Fluid Mechanics. John Wiley and Sons, Inc. New York.
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1965 Effectiveness of Jets Produced by Fan-Beffle Arrangement in
Mixing and Distributing Ventilation Air. American Society of
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1960 Housing Design and Equipment for Economical Broiler, Egg

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Taylor, G. I.
1921 Diffusion by Continuous Movements. Proc London Math. Soc. Ser.,
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men use 0w