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HEAT TRANSFER THROUGH AN AIR CURTAIN

-CD#—‘

Thesis for flue Degree of M. S.
MICHIGAN STATE UNWERSITY

Gad Hetsroni

1960

Ill Ill/II 11/ I liflll/Mgflflflflflflllllfl/Isflfl/flll

This is to certify that the
thesis entitled

"Heat Transfer Through an Air Curtain"

presented by

Gad Heteroni

has been accepted towards fulfillment
of the requirements for

14.3. degree inAgéicutuml Engineering

 

Jan/3% W

Major professor

Date Z/’/60

0-169

 

 

oivé/

 

 

OVERDUE FINES:

25¢ per day per item

RETURNING LIBRARY MATERIALS:
Place in book return to remove
charge from circulation records

 

HEAT TRANSFER THROUGH AN AIR CURTAIN

by
GAD HETSRONI

AN ABSTRACT

submitted to the College of Agriculture and College of
Engineering of Michigan State University of
Agriculture and Applied Sciences in.partia1
fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

Approved by W 7/16/0

September 1960

 

ABSTRACT

The objective of this investigation was to determine
the heat transfer characteristics of a vertical air stream,
considering (1) the effect of air velocity and (2) the
effect of the depth of the air stream.

An air curtain model was constructed in an opening
between.two constant temperature chambers. A temperature
gradient across the curtain was maintained and the heat
quantity transfered through the curtain was measured
for various depths of air stream and for various air
velocities.

The over-all heat transfer coefficient was calculated
and plotted versus the Reynolds number of the air stream.

An equivalent heat transfer coefficient for unit
depth of air stream was suggested.

A dimensionless ratio characterizing the heat transfer
through a vertical air stream was formed. This ratio,
denoted by H, was plotted versus Reynolds number of the
flow. A formula describing the curve thus obtained was

determined.

HEAT TRANSFER THROUGH AN AIR CURTAIN

by
GAD msaom

A THESIS

Submitted to the College of Agriculture and College of
Engineering of Michigan State University of
Agriculture and Applied Sciences in partial

fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

 

Approved by (MM (5)5454 9/14/0

September 1960

015mb}

(1'1‘

ACKNOWLEDGEMENTS

The author wishes to express his appreciation to
Dr. Carl W. Hall, whose guidance and encouragement made the
investigation rewarding and enjoyable.

Grateful acknowledgment is also due to Dr. Fred H.
Buelow for his assistance in the experimental set-up and
guidance in intrumentation.

The author is indebted to Dr. Arthur W. Farrell, Head
of the Department of Agricultural Engineering, for making
available the graduate teaching assistantship that made
the undertaking of the investigation possible.

Mr. James<3awood and Mr. Glenn Shiffer of the research
laboratory are thanked for assistance and cooperation
during the investigation. ‘

The author wishes to express his gratitude to the.
American Air Curtain Corporation, St. Louis, Missouri, for
providing the air curtain model which was used in this
investigation.

Acknowledgement is also give to Beatrice Foods Company,
which through Dr. G. C. North, coordinator, gave initial
financial support.

The author would also like to express his appreciation
to his wife, Ruth, for her patience, encouragement and
assistance which helped make completion of the investigation

possible.
ii

CONTENTS

PAGE

sumw. O O I O O O O O O I O O C O O O O O O O O O 0
L1 st or Pimes O O C O O O O O O O O O O O O O O O O O
IntrOduCtion O C O O O O O O O O O C O O O O O O O O 0

Review of Literature . . . . . ... . . . . . . . . . .

CD-P'WNH

Equipment. . . . . . . . . . . . . . . . . . . . . . .
Procedure. . . . . . . . . . . . . . . . . . . . . . . 12
Results and Discussion . . . . . . . . . . . . . . . . 16
Summary of Results . . . . . . . . . . . . . . . . . . 31
Conclusions. . . . . . . . . . . . . . . . . . . . . . 32
Recommendations for Future Study . . . . . . . . . . . 33
References . . . . . . . . . . . . . . . . . . . . . . 3h

Appendix 0 O O O O O I O O O O O O O O O O O O O O O O 35

iii

SUMMARY

An air curtain was installed in an opening between
two insulated chambers. The air flow pattern and the heat
transfer-mechanism through the curtain were determined
for various air velocities and depth with the air moving
vertically from top to bottom of the chamber.

The profile of the air flow is approximately parabolic
by nature. As the air stream progresses away from the
outlet it becomes wider and the profile of velocity'
distribution becomes flatter. The Reynolds number of the
flow, from outlet to inlet grille, does not change A
considerably.

For air velocities of about 200 fpm to 700 fpm the
over-all heat transfer coefficient is preportional to
the air velocity and inversely proportional to the depth
of the curtain. The values encountered in this investigation
ranged from 5.0 to 16.0 Btu per hr. sq. ft. 9?.

The ratio of over-all heat transfer coefficient to an
equivalent heat transfer coefficient for a certain depth
was denoted by H and plotted on. semi-logarithmic paper
as a function of Reynolds number.

The formula to fit this curve isv

H = 0.5 6-1.8/Re x 10"Ll

This curve is asymptotic to the value of H=O.S, with

a very little variation in H for Re>12 x 10,4,
1

FIGURE
1.
2.

A- 8.
A- 90

A‘lOe
A-11e

A-12.

LIST OF FIGURES
PAGE
Experimental set-up used for the investigation 9

Arrangement of thermocouples in the air curtain
used during this investigation . . . . . . . . 11

Set-up for air velocity measurements . . . . . 13

Plot of U-value as a function of Reynolds
an e r O O O O O O O O O O O O O O O O O O O O 21’.

Plot of H-value as a function of Reynolds
timber O O O O O O O O O O O 0 O O O O O O O O 28

Air velocity distribution for curtain operating
in room; 1 nozzle (hS volts) . . . . . . . . . A2

Air velocity distribution for curtain operating
in room; 3 nozzles (60 volts). . . . . . . . . M3

Air velocity distribution for curtain operating
in room; 6 nozzles (115 volts) . . . . . . . . Ah

Air velocity distribution for curtain operating
between chambers; 3 nozzles tests (h5, 60 and
7S VOltS) e e e e e e e e e e e e e e e e e e e us

Air velocity distribution for curtain operating
between chambers; 3 nozzles tests (90, 115 and

lho volts) . . . . . . . . . . . . . . . . . . us
Air velocity distribution for curtain Operating
between chambers; 6 nozzles tests (60, 90, 105

and 115 volts) . . . . . . . . . . . . . . . . M7

Plot of the air velocity and Reynolds number
versus the voltage . . . . . . . . . . . . . . MB

Air temperature distribution (Tests 3 and 5) . ug
Air temperature distribution (Tests 6 and 7) . 50

Air temperature distribution (Tests 8 and 9) . 51
Air temperature distribution (Tests 10 and 11) 52

Air temperature distribution (Tests 12 and 13) 53
2

INTRODUCTION

Cold storage and work areas should be as accessible
as possible to workers. Entrances to storage and work areas
are necessary, however, and a side hung swinging door is
customarily used. Frequent Openings of the conventional
door cause air changes inside the storage area, which
introduce refrigeration losses and load the compressors.
Recently there has been much interest in the use of
air curtains, or a stream of air as a means of thermally
closing entry ways while allowing doors to remain
completely unrestricted for workers to enter and leave
as appropriate. '
The conventional air curtain consists of a vertical
downward flow of air across an.opening, providing a
barrier which can be penetrated by solid bodies only,
but not by insects.
Little data are available on the heat transfer
characteristics of air curtains. Since such information
is essential in design of this kind of closure, the objective
of this investigation was to measure the heat transfer
characteristics of air curtains, considering (l) the effect
of air velocity and (2) the effect of the depth of the

air stream.

REVIEW OF LITERATURE

Large refrigeration losses are often encountered from
air changes in cold storage rooms, or air conditioned areas.
The number Of air changes per day in such places depends
of the volume considered and to a large extent on the
number of door Openings per day. Wherever heavy traffic
is encountered, particularly entrances that require
Opening and closing of heavy doors, these losses might
be very costly. Large losses may prevent the refrigeration
unit from pulling down the extra load and from maintaining
a uniform and constant temperature inside the room.

Williams (1958) studied refrigeration losses through
the door Openings and conveyor passes into cold rooms in a
dairy plant. ‘Under normal Operation conditions fer a
38°F room, losses through a h2 in. x 78 in. door ranged
from 722 Btu tO 951 Btu per min. Losses through conveyor
passes ranged from 1&5 Btu per mine if the pass was
located 30 in. above the floor, tO 200 Btu per min. for
passes located 10 in. above the floor.

When a nylon curtain was used instead Of the
conventional door, temperatures in the cold storage room
were maintained constant but 70 percent increase in
compressor's operation was required. His Observations

were made using a diverted air flow technique in which

h

air from a blower was directed down across the door
Opening at 900 ft. per min. The air was recirculated
through a false floor and suction fan. Refrigeration
losses through the Open door were reduced from about 950
Btu per min. to 200 Btu per min. A 20 percent reduction
in compressor Operating time was Observed when the door
was closed at night and the diverted air flow technique
employed during the day.

The concept Of an air curtain is not new by any means.
A patent for a device tO seal an entrance from outside'
weather by means Of air flow, was issued to T. Van Kennel
in 190h by U.S. Patent NO. 77h,730 November 8, l90h
(Norton, 1959). The Van.Kennel air curtain consisted of
air streams introduced from both sides Of an entrance from
nozzles tO counteract wind forces blowing through the
entrance. Since then the idea has been successfully
adapted in Switzerland and England. Since 1952 air curtains
have been used in the United States-mainly in department
stores and banks. There is an air curtain hl ft. wide in
Reno, Nevada, and there is an air curtain 18 ft. high in
Lynn,‘Massachusetts. A more recent use is an 89 ft. wide
entrance closure Of Pan American's air terminal at
Idlewilthirport, New'York, as described by Norton (1959).

Gygax (1957) presents the principles Of the air
curtain as follows:

A series Of nozzles above the entrance discharges
layers Of air downward tO an air return grille in the

floor. The air is returned to the tap nozzles through

ductwork which contains filters, heating and cooling

elements, and blowers. This moving curtain of air
has sufficient depth to protect and insulate the store
interior from outside temperature, dust, dirt, rain,
snow, debris, insects and unwanted animals. Persons
passing through the air curtain feel a gentle breeze
and a pleasant sensation of warmth in the winter and
coolness in the summer.

The advantages Of Open entrances sealed by an air
curtain include: saving valuable floor space near entrance,
eliminating door maintenance and repairs, eliminating door
accidents, and reducing heating or cooling losses where
heavy traffic is encountered, particularly in cold storage
rooms and walk-in freezers which normally require heavy
doors.

There is only very little technical data presented in
the literature concerning the air velocity, required
thickness of the curtain and temperature Of air.

Cadiergues (1957) suggested a limit or 2,000 ft. per
min. at head level. Air temperature at this level should
be around 88°F. The discharge Opening should preferably
be a long slot with the duct having the same cross section
throughout. The cross sectional area Of the duct should
not be less than 2.5 times that Of the slot. The return
grille should be about three to four times the width Of the

discharge slot. The discharge air volume may vary from
1,500 to 15,000 cfm per linear foot Of Opening. Some
commercial systems use 1,000 cfm.per linear foot Of Opening

and a higher air velocity (believed to be one ft. deep).

NO data concerning the heat transfer pattern and the
insulation value of an air curtain were found in the
literature. To the knowledge Of the author, there is nothing
in the literature to suggest that research work with the
purpose Of the present investigation has been previously

undertaken.

EQUIPMENT

An air curtain model, supplied by the American Air
Curtain 00., was used in this investigation. The air is
forced through an adjustable distributor forming six
nozzles, (Figure l) . An air curtain is formed which has
a vertical cross-section of 7.75 sq. ft. (32.5 in. wide
and 3h.3 in. high). A plastic sheet divided into grids
covers one edge Of the curtain.

The distributor is Operatively connected by means of
a servo motor to a control mechanism. The flow of air
forming the air curtain is produced by four fans driven
by four 1/15 hp electric motors. Two fans draw the air
from the inlet chamber and deliver it through a duct to
the outlet. chamber. The two other fans are located above
the outlet chamber and accelerate the air into it. Thus,
the air flows in a closed circuit.

The air velocity of the curtain is controlled by the
speed Of the fans and can be varied by means of an
.autotransformer (Variac) in the electrical circuit.

The curtain was Operated with the distributor directing
the air in a vertical stream.

The air curtain model was placed between two insulated
chambers. The one on the right in Figure l is a cold
storage room normally maintained at 140°? by a ‘F-12

8

1‘ till '» " ‘
.. i

- ._..-
V '1' k

. . '1'

 

A

., , ,7
. yl I. 4 v, ‘ A
a}? -,- ~ u 7 .-

Figure 1. Experimental set-up used for the investigation.

10

1

refrigeration unit driven by 5 hp electric motor. 0n the
other side a 2 ft. x 2 ft. x 2 ft. box, constructed of % in.
plywood with 6 in. redwood fiber insulation, was maintained
at 85°F by a 1310 watt, 230 volt electric heating mat.

Instrumentation - a) The Operation time of the refrigeration

 

unit was recorded by an operation recorder and measured
with an electric clock connected in parallel with the
compressor.

b) The heating time and energy used by heating mat were
recorded and measured by means of an operation recorder
and watt-hour meter.

0) The temperatures at various locations were sensed with
copper-constantan (1938 calibration: 2h B & S gauge)
thermocouples, and recorded every hour by a recording
potentiometer. An automatic switch was used on this
recorder to enable the use of 32 thermocouples and to
operate the recorder every hour. The thermocouples and
recorder were checked for proper wiring and Operation
prior to measurements. The location Of the thermocouples
is shown in.Figure 2.

d) The speed of the fans was controlled by a Variac. The
voltage was measured with a Simpson meter and the speed

of the fan.was measured with a Strobotac.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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FIGURE 2. ARRANGEMENT OF THERMOCOUPLES

PROCEDURE

A series Of tests on air velocity were first run to
obtain air velocity patterns for three depths (variable
horizontal cross-section) Of the curtain. The velocity
at each.point was determined by means of a Pitot tube
and inclined manometer. Measurements were taken at the
‘middle plans of the curtain, every two inches in.height
and every inch in depth. The values are an average with
respect to time, and particular care was taken to Obtain
reproducible values. The accuracy Of the readings was
usually : 0.001 in water column.

The set-up for velocity measurement is shown in
Figure 3.

At the same time a closed door test (Test 2) was run
to determine the heat losses from.the constant temperature
box and the Operation time of the refrigeration unit of
the cold storage room, The constant temperature box was
fastened to the door Of the cold storage room (3/h in.
plywood, h in. redwood fiber insulation, 1/2 in. plywood).
The energy used by the box to maintain the constant temperature
Of 86 t 19F. the Operation time Of the compressor of the
refrigeration unit and the temperatures inside and outside
the chambers were recorded daily with seven replications.

Later an Opening of 7.75 sq. ft. (32.5 in. wide; 3h.3 in.

12

13

Y... . eh.
,i
am. am i

it!!!“

 

haunt

Set-up for velocity measurements.

F191” 3e

1h

high) was cut in the door and the air curtain model was
fastened to it. The constant temperature box was fastened
to the Opposite side of the curtain. The thermocouples
were placed in the curtain and connected to the recording
potentiometer.

Three of six outlet nozzles were blocked and the inlet
chamber grille was covered except for an opening 10 in. wide,
.below the three unblocked nozzles. The curtain was then
run six times, tests 3, 5, 6, 7, 8 and 9. The velocity
of the fans was changed after each test by means Of the
variable autotransformer (Variac). The voltage on the
Variac outlets, temperatures in.the cold storage room, in
the constant.temperature box, in the air curtain and outside,
the operation time of the compressor and energy used by the
constant temperature box, were recorded daily, with five
replications for each test.

After the series of tests with three nozzles were
completed, the air velocity distribution was determined
again for the various voltages. Whereas previous air
velocity patterns were determined with the same temperature
on both sides of the curtain, the air velocity pattern
was determined with the curtain installed on the cooler
and with the temperature difference maintained. It was
necessary to enter the cooler to make the Pitot tube
measurements in the air stream. Measurements of the air

velocity were taken every inch in width and on.three levels

15

Of height at the same levels at which the temperature
measurements were made, i. e., 56 in., 146 in., and 35 in.
from the floor.

Later the covers on three nozzles and on the grille
were removed and the series of tests with six nozzles were
conducted- The same. data as for previous tests were
recorded daily with five replications for each test (Tests
10, ll, 12 and 13).

After these tests the air velocities were determined
in identical manner as for three nozzles. Again special
care was taken to assure that the manometer readings were

reproducible .

RESULTS AND DISCUSSION

Air Velocity Distribution

The velocity at various points was calculated from

the data Obtained by the measurements with the Pitot tube.

The calculations.were based on the formula

where V1
C

h.

 

V1: Cfidm v g h
velocity Of flowing gas, fps.
velocity coefficient Of the Pitot tube.
In this case the Pitot tube hpd a long
impact-opening extension and a value
1.0 can be used for C (Eckman, 1950).
density Of manometer fluid, 62.3 lb.
per cu. ft. for water.
specific volume of flowing gas, 13.5 cu.
ft. per lb. for air at 709? and 50%
relative humidity.
acceleration of free fall, 32.2 ft. per

sec. per sec.

- manometer differential, ft.

With appropriate values the formula simplifies to

where V
h.

v = uoog/fi (1)

- velocity of flowing gas, fpm.

- manometer differential, inches of water

column.

16

17

The air velocity measurements were performed at the
middle plane of the curtain. It was Observed that air
velocity was higher closer to the air return.duct and
somewhat lower further to the front (Figure 3). It was
then.assumed that the middle plane would yield an air
velocity which would be average Of the whole width Of
the curtain.

The air velocity pattern was determined for two
different set-ups. One series of tests was first conducted
to obtain the air velocity distribution as occurs in a
curtain Operating simply in a room with no pressure
difference on.both sides of the air stream. The results
thus Obtained were plotted in.Figures A-l, A-2 and A-3.
These figures are in the form of charts with constant
velocity lines.

By studying these figures some general facts can
be observed:

1. As the air stream.progresses away from the outlet
it becomes wider, and the profile of velocity
distribution becomes flatter. This is due to the
increase in mass Of air flowing in the jet and
decrease in the maximum.velocity, according to the
‘momentum theory: RV = constant.

2. Cross section of the velocity map yields a velocity
distribution somewhat similar to a parabola with
the highest velocity at the center of the air stream.

18

The air flows in a way similar to a stream of air
in a slightly diverging duct.

The nozzles form a kind Of Obstacle in the air
stream, Negative pressure zones, due to eddies,
can be noticed near the outlets. At lower levels
the flow is nearly parabolic again, even at multi-
nozzle stream.

At about half way from.nozzles to the grille the
air stream develops a bend. The stream then
reforms in its original path.

A smpke gun was used for some Observations and an
air spill was detected in a zone high about six
inches from the grille. Above this zone, and
mainly near the nozzles, air was entrained into

the stream.from.the outside.

The above facts suggest several conclusions concerning

the air

1.

aflow’pattern:

The air flow is approximately parabolic by nature
and does not consist of several independent streams
flowing from.severa1 separated nozzles Operating
in parallel.

The fans at the air outlet chamber accelerating

the air downwards are more effective than the two
fans in the inlet chamber.

The Reynolds number of the flow does not change
considerably from the nozzles to the grille. The

19

decrease in air velocity is compensated by the

increase in hydraulic diameter.

.Another series of tests (Tests 3 and 5 through 13) was
conducted with the air curtain operating between the constant
temperature box and the cold storage room, A temperature'
gradient, and probably a pressure gradient also, existed
across the air streamt

Manometer readings were taken and velocities calculated
for air streams out Of three nozzles and out of six nozzles,
each.at various fan speeds and each at three heights from
the floor.

The depth Of the air stream at the various levels was
taken as the distance between the two points on both sides
of the air stream.where the manometer readings were
approximately zero.

The results are presented in Figures A-h, A-5 and
A-6. An average air velocity and depth of curtain for each
level was then calculated. These were averaged to get an
average air velocity and average depth Of curtain for
each test.

From this average a Reynolds number was calculated

for each test. The formula used was

VDH
1163-5- (2)
where Re - Reynolds number, dimensionless.

V - average air velocity for the test, fpm.

20

DH - hydraulic diameter, ft.

= h A g 2 x depth of curtain x width
DH P (dSpth + width)

u - kinematic viscosity sq. ft. per min.

A value for air at 70°F Of 9.9 x 10'3 sq.

ft. per min. was used.
These numbers are summarized in Table 1 and in Figure A-7.

The maximum percentage error for the hydraulic diameter

was estimated to be about 10 percent, that of the velocity
about 2.5 percent and of Reynolds number about 13 percent.
A sample calculation is presented in the Appendix.

Temperature Distribution

The temperature in the constant temperature box, in
the air stream and in the cold storage room, were recorded
every hour by means Of the thermocouples and a recording
potentiometer.

Ten hourly series of recordings were chosen, in.the
day that had the closest U-value to that test'average.
The values for the various thermocouples were averaged
from the ten readings and the temperature distribution
determined for that test.

The temperature distributions thus Obtained are
presented in Figures A-8 through A-12.

It is worthwhile to mention that the temperature in
the constant temperature box was kept fairly constant but

the temperature in the cold storage room varied from test

21

to test and was dependent on the U-value of the air curtain.
The reason was that the refrigeration unit, though Operating
continuously throughout all the tests, did not succeed in
pulling down the load and in maintaining constant temperature

in the cold storage room.

Over-all Heat Transfer Coefficient (U)
In steady-state one dimensional heat conduction the

formula used is

q=UAAt (3)
or

q=UA(th-tc) (it)
where q - conducted heat quantity. Btu per hr.

- cross sectional area (height x width of
Opening), sq. ft.
th - temperature at the warm side, 9F.

temperature of the cold side, 9F.

('9’
O
I

U - over-all heat transfer coefficient, Btu
per hr. sq. ft. oF.

Solving equation (h) for U yields
(5)

 

, q
Mth - 1:6)

The value for A = 7.75 sq. ft. was Obtained by
measuring the cross sectional area of the air curtain
(width x height).

The value for q was Obtained by measuring the energy

input in the constant temperature box. The value measured

22

was kilowatt4hr. per hr. This value, converted to Btu
per hr. by multiplying by conversion factor of 3h13 Btu
per kilowatt-hour, was called q'.

From.this quantity the heat quantity transferred by
radiation (qr) was subtracted. This quantity was calculated
by

qr == Fe Mn,“ - Tau) (6)

where F - a modulus which modifies the equation for
perfect radiators to account for emissivities
and shape factors, assumed to be one,
because the chambers were approximately in
shape of cave with wood and pitch walls.
C - Stefan-Boltzmann constant 0.171h x 10'"8 Btu
per’hr. sq. ft. Ru.

Th, Tc - absolute temperature Of warm and cold sides, °R.

Another quantity subtracted from q' was the heat
quantity lost to the room, which was determined in Test 2
the closed door test. This quantity was assumed to be
constant for all tests and a value of q1 = 80 Btu per hr.
was used.

The heat quantity transferred through the air curtain
by combined mechanism Of convection and conduction was
denoted by q and is

q'q'-qr-ql (7)
substituting the value thus Obtained in to equation (5)
yields the U-value for that particular day.

23

The accuracy of U-value was then statistically
determined. A sample calculation is presented in the
Appendix.

The values obtained for the over-all heat transfer
coefficient and the confidence limits are summarized in
Table l. The over-all heat transfer coefficients are
plotted on semi-logarithmic paper in Figure h.

The plot of U-value for three nozzles in Figure h
shows a trend of the curve to become asymptotic to the
value of‘U=15 Btu per hr. sq. ft. °F. Bearing in mind
the fact that the number of observations in this investigation
was not large enough to prove this fact, a general conclusion
may be suggested: When Reynolds nwmber reaches a certain
value or the air velocity reaches the value of about 650 fpm
for this depth, the flow is fully turbulent with fully
developed eddy currents flowing throughout the air stream.

This hypothesis is further developed in the following

paragraphs.

Equivalent Heat Transfer Coefficient (L)
In steady-state one dimensional heat conduction
through a medium the formula used is

dt

where k - the unit thermal conductivity, Btu ft. per
hr. sq..ft. OF.
A - area, sq. ft.

-%£ - temperature gradient, 9F.

 

 

 

 

 

r—- ] 1— ] I I I r | I ,
I1.
32; O——0 3 NOZZLE CURTAIN
m: A——--A 6 NOZZLE CURTAIN
3 e
r W 1
G
8 ~ ._
>- ’A’AZ/
6 r ,A/’/ ‘
. / A 1
4 _. _
- 4
2 r- _
L . J 4 L 1 1 l 1
3 5 7 9 n
-4
Re xlO
FIGURE 4 SEMI-LOG PLOT 0F U- VALUE

VERSUS REYNOLDS NUMBER.

25

The k-value for still air at 70°F is as low as 0.015
Btu per hr. ft. 9F, which.could not cause the rather high
U-values experienced in this investigation. It was assumed
therefore, that an equivalent coefficient for heat transfer
through flowing air should exist. This coefficient was
denoted as L and has the units of Btu ft. per sq. ft. hr. 9F.

Equation (8) could then be modified to

q-LAAt (9)

or

q
L = m (10)

The L-value for each day was obtained in a similar
manner to the U-value, except for the temperature gradient
term. This gradient was established from the temperature
distribution in the air stream.(Figures A-8 through A-12
in the Appendix) as an average of the three levels. The
temperature gradient was obtained for a depth of 6 in.
for the three nozzles curtain and lh.h in. for the six
nozzle curtain, allowing some depth for the boundry layers
of the air stream.

The appropriate values were then substituted in
equation (10) to obtain the L-value for each test.

A sample calculation is presented in the Appendix.

The results are summarized in Table l.

The method used to obtain the L-value is not precise
by any means and the values thus obtained could serve as an

approximation only. A more precise analysis has to consider

26

mass transfer, air velocity, rate of turbulence etc. This
could have not been done with the limited number of

observations in this investigation.

H-Ratio

To generalize the results obtained in this investigation
a dimensional analysis was carried out.

The dimensionless number that includes most of the
‘units that characterize the flow is the Reynolds number
(Re). The pressure gradient that exists in the air stream
was neglected here, though it might be of some importance
in practical applications of air curtains.

Another dimensionless number resulting from the
analysis was the ratio of the over-all heat transfer
coefficient to the equivalent heat transfer coefficient for
a certain depth of air stream. This number was denoted
as H and is defined as

.U
H = i no (11)

where H - dimension less ratio.
U - over-all heat transfer coefficient, Btu per
hr. sq. ft. 9?.
L - equivalent heat transfer coefficient, Btu
per hr. ft. 9?.
Do‘ depth of the air stream when emerging from the
nozzles, ft.

The H-number for the various tests was calculated

27

using U-values for each test and an average L-value. The
variation of L-value for the various tests was of such
magnitude that an average of all the tests (L 8 20.9 Btu
per hr. ft. 9?) was assumed to be as close as possible
to the precise value.

The D-values used were 0.625 ft. for the three nozzle
curtain and l.h ft. for the six.nozzle curtain.

A sample calculation is presented in the Appendix.

The values thus obtained are summarized in Table l
and plotted on semi-logarithmic paper in.Figure 5.

The formula for the over-all heat transfer coefficient,

 

 

U, is
l
U = A— (12)
‘E + l + l
'51 52
where hl’ h2 = surface unit conductance, Btu per hr.
sq. ft. 9?.
assuming h1 B h2 = h
gives
_ 1
"'2+§ ””
L h
but
h-L um
'2

where x - thickness of boundry layer, ft.
substituting eq. (It) in eq. (13) yields

H RATIO

'5
L 8

 

 

 

 

 

 

 

1 l l I I 1 I I i
2.0.. 0—0 3 NOZZLE CURTAIN _
A—A 6 NOZZLE CURTAIN
l-O - _
.6 _. _1
A A 4&9 A
4 '- . Q —T
/ A
.2 — __1
I 1 l 1 1 1 1 1 1
3 5 7 9 ll
-4
Re; l0
FIGURE 5 SEMI-LOG PLOT OF H-RATIO

VERSUS REY N OLD S

NUMBER.

29

U = ---§- (15)

L

l
4.

EM:

substituting equation (15) in equation (11) yields

U D D D
H = O .. O = O (16)
L (2+§)L D+ 2x
L L

 

 

 

for air streams of high velocity when the nozzles are not
very high above the grille, or for large Do values, it
can be assumed that D = Do'

Equation (16) then becomes

H = 1 (17)
1' +' fii

 

It is worthwhile to study one extreme case in this
equation: When D = 2x equation (17) becomes H = 0.5.
This merely means that the boundary layers, from two sides
of the stream, meet somewhere in the middle of the air
stream. The hypothesis that the flow becomes fully mixed,
with fully developed eddy currents that run from side to
side, at about Re = 12 x 10h (for a three nozzles curtain)
was previously stated.

The U-values Obtained for a Reynolds number of about
11 x 10h was U = 15 Btu per hr. sq. ft. 9? when D = 0.625
ft. and L = 20.9 Btu per hr. ft. OF then

H = 15 I 0.625 3 0.145
20.9

which is close to the value obtained using a theoretical

30

approach.
The formula that seems to fit this curve best, for
the range Of Re 8 2.5 x lOLL to Re = 11.5 x 10“ is

-l.8/Re x 10‘“
H = 0.5 e

This formula describes a line asymptotic to 3.8 0.5,
as suggested by the theoretical approach. The range of
Re<2.5 x 101‘ was not tested in this investigation and no

data are available to verify the suggested formula.

31

 

 

 

 

 

 

 

 

 

3mm. 95.. S. M 9m 2.0 so: £4 m: e S
23. s.m~ R. H as «3. gm 8; m3 s 2
:3. Tom 81 H ms 26 3: mm; 00 e 2
8m. m.m~ on. w. lam . Rd mom em; 8 0 NH
mam. has fl. H 0.2 8.: £3 om; m9 m a
:2. mg: no. H m1: 3.: m2 £4 m2 m m
93. L23 om. H fima 8.3 0.3 :4 oo m e
oi. TS 2. H 3: 8.3 gm an; m» m a
non. TS S. H Qua «Tm mmm 1:; 8 m m
mam. Rom om. H To 09m so” 36 m: m o
m .H 1m :13 x on a; Sad o 3%» sMMsmwm paw”
EmomwmeHH (I.

 

 

memes no hadssam

.H OHQCB

CONCLUSIONS.-

The profile of the air velocity in the curtain is
approximately parabolic and does not consist of several
independent streams emerging from separated nozzles
Operating in parallel.

As the air stream.progresses away from the nozzles it
becomes wider, and the profile of velocity distribution
becomes flatter. The Reynolds number of the flowing
air remains approximately constant.

For the velocities tested the over-all heat transfer
coefficient is proportional to air velocity and
inversely prOportional to the depth of the curtain.

The values of the over-all heat transfer coefficient
obtained were from 5.0 to 16.0 Btu per hr. sq. ft. °F
for a depth of 0.97 to 1.81 ft. and for an average
velocity from 189 to 673 fpm.

The ratio of over-all heat transfer coefficient to the
equivalent heat transfer coefficient (a value of 21 Btu
per hr. ft. OF was used) for a certain depth of curtain
was found to characterize the heat transfer through an
air curtain. This ratio was denoted by H.

The H ratio is related to Reynolds number of the flow

by the formula

H 1. 0.5 e-l.8/Re x 10"h

32

RECOMMENDATIONS FOR FUTURE STUDY

Determine U-values for higher air velocities and larger
Reynolds numbers.

Verify the equivalent heat transfer coefficient for air
streams at various velocities.

Determine the effect of air curtains with air streams
at low velocity introduced in the doorway opening from
nozzles at the top and at the two sides.

Estimate the costs of air curtains with various
combinations of depth and air velocity. Plot the
expenses and savings in cooling versus various curtains

and find the break-even point.

33

REFERENCES

Anonymous (1956) Entrances are sealed behind air curtains.
‘Refrigeration Engineering 6h(h):h9.

Anonymous (1957) Doorways of air. Science Digest hl:92.

Anonymous (1959) Modern production technique demand warm'
air curtain. Heating and Air Treatment Engineer

Cadiergues, R. (1957) Warm air curtains. Heating and
Ventilating and Journal of Air Conditioning 30:h23.

Eckman, D. P. (1950) Industrial Instrumentation. John
Wiley and Sons, Inc., New York, New York.

Gygax, E. E. (1956) Air curtain seals door Opening.
Heating, Piping and Air Conditioning 28(1):1h -1h7.

Gygax, E. E. (1957) Air curtain entrances ow wider.
Heating Piping and Air Conditioning 29 10):12h-l26.

Hall, C. W. (1957) Reducing refrigeration costs in the
dairy plant. Journal Of Dairy Science 60(h):h33-h3h.

Jakob, Max (1957) Heat Transfer, Vol. I. JOhn Wiley and
Sons, Inc., New York, New York.

Norton, W. (1959) Where to use a curtain Of air. Consulting
Engineer 11(3):lO8-ll3.

Nottage, H. B. (1951) Ventilation Jets in Room Air Distribution.
The.American Society of Heating and Ventilating
Engineers, Cleveland, Ohio.

Steiner, E. (1958) Device for producing a roompclosing air
curtain. U.S. Patent No. 2,863,373.

Williams, R. M. (1958) Refrigeration losses through Open
doors and conveyor passes. Unpublished Thesis for
M. S. Degree, Michigan State University, East Lansing,
Mi chigan .

3h

APPENDIX

35

SAMPLE CALCULATIONS
A sample calculation is given for Test 7.

1. U-value

Energy consumed by heating element in constant
temperature box - 19.1 kilowattéhr. per 25.02 hr. or
q' = .763 kilowatt-hr. per hr. = 2600 Btu per hr.

The temperatures in cold storage room, and in constant

temperature box, as averaged from 25 recordings

th = 87.11%; t0 = 611.3%; At = 23.1%

Heat transferred by radiation
qr=FxCxA(Thu-Tcu)=

3 x 7.75 (5117“ - 5211”) =

= 1 x 0.171h x 10-
= 200 Btu per hr.

Heat losses to room, q1 = 80 Btu per hr.

Heat transferred through curtain by conduction and

convection -

q = q' - qr - q1 I 2600 - 200 -80 =

= 2320 Btu per hr.
The over-all heat transfer coefficient for that day,

using equation (5):

U:

 

q 8 2320 - 13 O Btu er hr 3
Aflw1 7.75 x 23.1 . ft, 8p, . q.

36

2. L-value

The temperature gradient

0
T .1 F
lé- a 7 ' = 1h.2 QB per ft.

 

15x 6 in.
q = 2320 Btu per hr. A = 7.75 sq. ft.
substituting in equation (10) ,
Q 2320

 

AA? = 7:75 2: 111.2

3. ngatio
Using the average of U-value for Test 7 and the

average L-value for all tests.

U a 13.0 Btu per hr. sq. ft. OF.

L = 20.9 Btu per hr. ft. OF.

no: 0.625 ft.

substituting in equation (11)

H = .% D0 = llaQ_§a9a§£5 = 0,389,

20.9

37

. 21.1 Btu per hr. ft. °R.

ACCURACY OF RESULTS

Accuracy of the results can be estimated after the
precision of measurements is estimated and the maximum

error calculated.

1. Velocity

 

v = Loos/E
_ 1005 (Ahl
um- L575.

assuming Ah = 1» 0.001 in. for h = 0.020 in.

v 1005/1? .. 567 fpm.

lAv|= ($995 x 0'0” = 1L1.2 fpm.
2 170.020

maximum percentage error

L—v 1:100 567 x100 2.5%

2. Hydraulic Diameter

 

_ A
thp
where A - cross section area of air stream = 3 ft. x
depth of curtain.

P - wetted perimeter of air stream = 2(3 ft. +

depth of curtain).

38

39

D - depth of curtain = 1 ft.IADI= l in.

 

A=3.0 sq. ft; (AAI=3x D=3x1=l/h sq. ft.
P=8.0 ft; IAPI=2x D=21-’§‘-1-=1/6 ft.

. 5. x3. . . 3
D11 up L5— 1.5rt.IADhI gun-+3111»:

hx1+hx3xl=

 

“ 5 11 TH“ E
= 0.156 ft.
IADhl 6
DB x100=9ޤ-x100=10.%

3. Reypolds Number
“311
3° = “11"
u = 9.9 x 10"3 sq. ft. per min. [Au]: .15 x 10"3 sq. ft. per min.
V = 567 fpm. |AV|= 111.2 fpm.
Dh = 1.5 ft. |ADA= 0.156 ft.

v 6 1.
=ih=§1§ S=8.6x10b'

Re
u 9.9 x 10"3

 

 

 

 

V V 1.5
a. = EHAVH 4A |+ 39mm.- x 111.2 +
u u Dh u2 9.9 x 13
+ 4576 3 x 0.156 + 567 x {a x 0.15 x 10"3 =
9.9 x 10" 98 x 10

h0

= 2.1 x 103 + 8.9 x 103 + 1.3 x 103 s 1.13 x 10h

h
IAReI x 100 g 1.13 x 10 a

13.2%
Re 8.6 x 10E

2L. Over-all Heat Transfer Coefficient (U)

The precision for the U-value was determined
statistically. A calculation example is given infiTest 7.
The figures are presented in the following table.

 

, U (01 - 0)2
13.1 .006u
13.3 .0785
13.0 .0008
12.8 .01185
12.9 » .01115
Total '\ 65.1 .1u83

6 = 93:1 - 13.02
5

 

E”2 ___ Sum of squares : £1.83 ‘ .037.
11

degrees of freedom
standard deviation s = .192
Taking level of significance a = .05 the Student's
t = 2.776 ’ '

The interval estimation of the results

v s 1.92
U=U ‘3 . .6=
i‘7; 1302::I1277

= 13.02 1..2h. Btu per hr. sq. ft. 9?.

 

hl

 

 

 

,' on 0
1n 0
( I' /\ I
. "o \/ \
o

)I v A 2'

0 o ‘
. ,3) g2 8k
'1 I ‘ J l \r ‘ I I v

4 8 IO I2 I51 6 IS 20
DISTANCE FROM HE [n.l
FIGURE A.l AIR VELOCITY DISTRIBUTION

I NOZZLE , 45 VOLTS

 

II II

 

_ RRRRRRRR \/

 

QIIW TH .

III M

\IIn

 

 

III/III

. WIIII IIBI
(III II III)
. . .IIIIII J/I'I II

DISTANCE FROM THE LEFT [in]

0"
A

.LIIEIILLIIWHWH 11...:
~ I \Kn‘jI (V); \I-I’: ‘3‘? w (I it) I
‘ Inn: ~’

« )ITII ' "I //
- )I‘ - I) .I

V

O
0

0|
0?

U.
N
/\
A
V -
-_/,’-
-../
f"
/ F

 

 

HEIGHT FROM THE FLOOR [inJ

.h

m

1 1 A
~\,/-"—" .

44«

40(<

36 / I

 

 

DISTANCE FROM THE LEFT Lin.)

FIGURE A.3 AIR VELOCITY DISTRIBUTION
6 NOZZLES , H5 VOLTS

VELOCITY Hum]

IIS

 

 

IOO"

 

 

 

 

 

 

 

 

 

60 VOLT: LEV—“3L3.
_ o—o 00h. "OI IL
1 5-4 “in. "OI rLoo
D-u-i 34in. "OI FLOOR
53004
:3
).
.-
u d
O
.J
In
>
200«
IOO'I
I'éI'cI'saz'Oiaiie EIOIEIKI'OI-zozzuzs
OIsnIIcE now TN! LEFT (IIIJ OIs'rANcE non THE LEFT tin.)
19.19.1111.

VELOCITY [fpm]

200«

 

 

 

 

0 IO (2 I3 I'e Ieioizi4ie
menace now me LE" tInJ

FIGURE AA AIR VELOCITY DISTRIBUTION
THREE N0zzLE CURTAIN OPERmNc
sETwEEN CHAMBERS.

VELOCITY Hum]

IIS

 

 

 

60 VOLT.

 

 

 

 

 

 

 

Y T T
I2 I4 I

DIsTANcE FROM THE LEFT tin.)

 

45 VOLTS
o—e “In. "on IL
1 5.-.; «In. new noo
eu-«e Min. "on FLOOR
£3001
-
H
)-
g.
0
O
..l
U
>
2004
IOO'I
iz'oz'zioie EITDAIEEEOEEEXEE
' DISTANCE ERON THE LEFT an.)
15:52ng

vELocITv [tom]

 

 

 

 

V

eIOIEMIB (050225423

DISTANCE FROM THE LEFT (In)

FIGURE AA AIR VELOCITY DISTRIBUTION
THREE N02 zLE CURTAIN OPERATING
BETNEEN cNANBERs.

Upm]

VELOCITY

 

I200<

lOOO‘

OOO‘

 

IIS VOLT S

II6

 

VELOCITY [1'me

 

 

 

 

O‘I'OIEI'OI'O

DISTAICE FEM

FIGURE A.5

90 VOLT!

o———o Ooin‘rnou FLOOR
b-m-J « In. "on noon

EFT-4 I. In. FIG. FLOOR

 

2‘0 2'2 54 20
TIIE LEIT (I...)

a IVOIVZIVQIYGIBZOIZZVAZYS
OIsTAIIcE non TIIE LEFT [in]

 

VELOCITY [fpml

 

 

 

 

THREE NOZ ZLE

III 20 a 54 20
IIIIOII THE LEFT no.1

DISTRIBUTION

CURTAIN OPERATI N G
CHAMBERS .

 

 

 

 

 

 

 

 

   

 

 

II?

 

 

 

 

 

 

 

 

 

,0 VOL" IO VOLTI
_ —
O—Q [Olml’m FLOOI
b—-—J 40 In no. FLOOR
Emu-l 34 h. FNON FLOOI
._ 000‘ -- ‘°°‘
E E
e 2
_. L.
: BOO-I I: goo.
6 5»
O
.1
.1 ; hm.
> , C
400‘ 400- K
n I.
ll \
.
300- loo~ I]
. H I
200. 200- I; ‘I
‘k
. ‘1
H’ ‘v
.00. I004 I: ‘.‘
. I
' \
I 1 II
. , I
A n
, , r I , I . . . I . . . I r
4 0 l0 I2 I4 Is In 20 22 24 ‘ ' '° '2 " " " '° 33 2‘
OIsTANCE FROM THE LEFT [in] ”"7““ "'0" "‘5 LE” “"1
no VOLT: IOU VOLT!
.. 000- ._ 000‘
E
2 §
> >
I_- 500-1 I: 000-
U 0
o ‘ °
-‘ a‘
‘;' >
400- 400-
300- 800‘
‘\
200'I \\ zoo-I
\ ‘I
Ioo- - \ I00-
\ I
' I
I
I
\ .
T 17 V Y I l I I v I I l I I I l
4 0 I0 I2 I4 I0 I0 20 22 24 4 0 I I0 I2 I4 IE I. 20 22 24
DISTANCE Fnou THE LEFT [in] DISTANCE FNON TNE LEFT [In]
FIGURE A.6 AIR VELOCITY DISTRIBUTION
SIX NOZZLE CURTAIN OPERATING
BETWEEN CRANBERS.

fpm

VELOCITY (V)

 

O——O 3 NOZZLE CURTAIN
A——-A 6 NOZZLE CURTAIN

 

700-
I/0\_v\-
/ \-~0 “
600- ’ -
Re
/ I 4%»
I 0 O
500 ._ / -
' Re A

300 - /

ZOO -- / '—

 

1 l J 1 l A g A 1 J

400 - / /A“\g__...V_——-————'——---‘A ..

 

 

4O 60 80 IOO I20 I40
VOLTAG E IVOIIs]

FIGURE A.7 . AVERAGE AIR VELOCITY AND
REYNOLDS NUMBER VE RSUS
THE VOLTA GE.

IO

[°F]

TEMPERATURE

 

L9

ALI II... II.

 

TEST 3

°———0 56" FROM THE FLOOR
A—fiu—A 46" FROM THE FLOOR

90- 0----Ja 34" FROIII THE FLOOR

 

 

 

 

 

 

T T T T T. I Y T I l
O 4 8 l2 I6 20 24 28 32 36
DISTANCE FROM THE LEFT [in.J

FIGUREA.8 AIR TEMPERATURE DISTRIBUTION

 

[° F]

TEMPER ATURE

.IILJILJI

 

 

 

 

 

TEST 6

- H 56" FROM 'THE FLOOR

&—-—A43" FROM THE FLOOR

90'J U a- ----- a 34" FROM THE FLOOR
I
80-
1
70‘I
604
90-«
80"
70%

 

 

 

 

I I T I I

I I j T I
O 4 8 I2 IS 20 24 28 32 36
DISTANCE FROM THE LEFT [in.l

FIGUREA.9 AIR TEMPERATURE DISTRIBUTION

[°F]

TEMPERATURE

 

TEST 8

o—m-o 56" FROM THE FLOOR
FROM THE FLOOR

goq a ----- a 34" FROM THE FLOOR

 

'70-I

60‘

 

 

70‘

60-

50‘

 

 

 

 

048'I'2 I6 20 24 28 32 are
DISTANCE FROM THE LEFT Lin.)

FIGURE A.IO AIR TEMPERATURE DISTRIBUTION

[°F]

TEMPE RATUR E

JIL—JIII—JIII—JIILJIIL—JIII

 

TEST IO

904 o——056" FROM THE FLOOR

A—-—A 46" FROM THE FLOOR
B———-{a 34" FROM THE FLOOR

 

 

 

 

 

6 0- \‘ \
%\:\\
.. \‘vé
0*, E
.A\ TEST II
eo~ K-B“~~~: .5 ‘
- o \ §3§:§.¢.
: \
\\\‘
70-- g
\\
\ \
60- \\\\ Ok
I ° ““““ +1
. L- .4
I F I F I I r r 1 I o

 

O 4 8 l2 I6 20 24 28 32 36
DISTANCE FROM THE LEFT [in]

FIGURE A.Il AIR TEMPERATURE DISTRIBUTION

 

[°F]

TEMPERATURE

53
“Jgfit IIII ALIA

TEST I2

0——-0 56" FROM THE FLOOR
A—--—A 46" FROM THE FLOOR

B—---fi 34" FROM THE FLOOR

 
 
   
  

 

 

TEST I3

 

 

 

I I 1 I I I ' I I I gL-J
O 4 B I2 IS 20 24 2B 32 36
DISTANCE FROM THE LEFT [in.l

 

FIGURE A.I2 AIR TEMPERATURE DISTRIBUTION

JUL 30 .1961
AUG—1W

"IIIIIIIIIIIIIIIIT