LIBRARY
COPY
HYDnRAliC GRADIEf
AND
OP ON A PERFORAD PLM
P$ISUHE
by
Robert T. Hucks,
Jr.
S.B., Lehigh University
(1950)
and
t
William P. Thomsonm
S.B*, Purdue University
_
(1948)
Submitted in Partial Fulfillment of the
Requirementsfor the Degree of
MA$2EROF SCIENCE
at the
MASSACHUSS
INSTT
1951
Signatures
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Signature of Supervising Professor
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52M-126
HYDRAULIm D=If
ANDPRESUE DROP
ON A PERAM
PLI
Robert T. Hucks,
r
Willian P. homson
By:
Submitted for the degree of Master of Science
in the Department of hemi cal Engineering at
the Massachusetts Institute of Technology on
August 24, 1951,
Hydraulic gradient and pressure drop on a perforated plate were
studied using a 120" x 1
A 60" :
10" section of the plate was perforated with 1/8" holes on 1/4"
equilateral
liquid
1/2" test section of 14 gauge sheet steel,
triangular
flow.
The inlet
enters, the long dimension being parallel to
and outletcalming sections were each 24" long,
All data were taken using a air-water system. The superficial
air velocity was varied from 57 to 7 ft per seej; water rate was
varied from 0 to 24 gpm/ift; and weir height was varied from 1/4 to 1".
Hydraulic gradient data were correlated using a anntring-type
friction expression:
}
ft Vf2 N
2g
rh
Whereft was correlated against Re':
Re3
rh Vf /f
52M-l 26
The pressure drop data were correlated using the following
expression for the drop through the perforations:
ho
CVp2
The total plate pressure drop was found to consist of this drop, a loss
due to suface tension effects, and a loss equivalent to the hydrostatic
head of the liquid above the perforationsa
Nethods were developed for predicting the hydraulic gradient and
pressure drop on a perforated plate operating in the range of variables
studied.
Thesis Supervisor: E. R. Gilliland
Title
Professor of ChemicalEngineering .
Chemical Engineering Department
Massachusetts Institute
of Technology
Cambridge 39, Massachusetts
August 23, 1951
Professor
;oseph S. Newell
Secretary of the Faculty
Massachusetts Institute
of Technology
Cambridge 39, Massachusetts
Dear Sir:
In accordancewith the regulations of the Faculty, this thesis,
entitled
"Hydraulic Gradient and Pressure Drop on a Perforated Plate,"
is hereby submitted in partial fulfillment of the requirements for
the degree of Master of Science in Chemical Engineering.
Respectfully submitted.
Robert T. Hucks, Jr.
William P. Thomson
A
-EWIEDg
The authors wish to express their appreciation to
Professor E. .his
R. Gilliland for
manyhelpful suggestions
in supervisingthis thesis.
Credit is also due to Mr. H. H.
Engineering Shop under the direction
their cooperation,
arter and the Chemical
of Mr H 0. Chasen for
TABIZ OF CONTENTS
Page
I
Sumary
o. . . .. .
.
II Introduction
.
.
*r
1
.
4
.
.
.
..
A. Object of the Investigation. .
Limitations of the Investigation
C.
Ter inology .
.
.
.
*
.
...
B,
.
Or I
. . .
..
D,
Previous
Wkork... c..... .. a...
III
5
7
8
Procedure
A. E
rerimental
Progra,
a
B. Description
Of aratus
.
*
O
.
O
a
.
a
16
.
. Experimental Procedure
a
s
.
.
.
.
.
a
.
D. Method of Correlation
1.
Hydraulic Gradient
2
Pressressure
Drop
IV Results
3
o.
19
21
.. .
.*o .o
15
..
£
8
0
0
a
a
a
a
*
*
a,
a
a
a
a
a
*
a
*
a
a
a
a
a1
a
0
21
22
0
23
V Discussionof Results
A. HYdraulic
Gradient
Correlation
B.
CI. Pressure
VI
VII
*
*
,e
Calculation Procedure
for Predicti
D.
.
rop Correlation
.
*
0
0
36
a
$
*
$
0
37
0
08
*
*
a..
**,*a
draulic Gradient
.
*
. . . ..
a
0
43
Pressure Drop Calculation Procedure
Conclusions
Recommendations
, *o .
*
. a ..
* *
o
·
*
*
.
S
*·
.
.
*
$
a
45
47
TABX
OFF CBNTfNT
(Continued)
Page
VIII
Appendix
SumnarizedGradient Data
. . .
a
a
a
a
ak a
a
8
Su;marized Pressure Drop Data . .
56
.
A. Saple
Calculations.
49
.
.
.
.
5
*
0
...
65
B, Plate Leveling Procedure . . .
67
0. Calibration of Flowneters . .
68
D, Nomenclature
.o . ,o
E. Literature Citations
a
..
.
a
.
a
a
a
a
a
s
89
a
*
a
a
a
a
a
a*
71
........
.
OF FIGLRMS
2
Figure
Page
1
Flow Diar
2
Perforated
Plate
3
Hydraulic
Gradient
4
Hydraulic Gradient vs. Air Velocity . ....
5
Pressure Drop on Dry Perforated Plate .
. .
.
6
Total Plate Pressure Drop vs. Air Velocity
.
7
Total Plate Pressure Drop vs. Water Rate
. .
. *
28
8
FrictionFactorCorrelation- f' vs. Re'
. . .. .
33
9
Friction Factor Correlation- f'T vs. Re' . . .
10
of Apparatus
Layout
. .
. .
.
..
vs. Water
Rate
. .
. . . .
. .
..
, .
.
* .
. .
Table
**..*.
18
20
24
25
26
27
35
.
PlatePressureDrop vs. Air Velocity . . . . . .
ID IX
40
OF TABLES
*
* .
A
Ia
Summarized Gradient Data
A
Ib
Sumarized Gradient Data - Calculated Results
A 3I
Summarized Pressure Drop Data - Dry Plate .
A III
SummarizedPressure Drop Data WaterRate.
Liquid on Plate - Negligible
A IV
.
Sumnarized Pressure Drop Data -
Plate. . . .
Liquid FlowingAcross
.
49
·*
53
·
0
s
* *
· ..
·
56
60
1
The successful operation of a perforated plate depends to a large
extent on the hydraulic gradient of liquid on the plate and the pressure
drop of the vapor in passing through the plate.
little
At the present time,
information is available in the literature concerningthese
phenomena and no satisfactory
method for predicting
them has been pro-
posed. The purpose of this thesis is to develop a practical method of
predicting the pressure drop andhydraulic gradient on a perforated
plate.
Data were taken using an air-water system and a perforated plate
having 1/8-inch perforations on l/4-inch equilateral triangular centers.
The range of operating conditions studied involved liquid rates up to
24 gpm/ft*, vaporsuperficial
velocities
up to 7 ft./see.,
and seals
up to 2 inches. This range was considered compatible with present day
commercialpractice in designing towers. Data were also taken using
the plate with no liquid on it.
The following conclusions for hydraulic gradient and pressure
drop on a perforated plate were drawn from the data of this investigation:
1.
The hydraulic gradient increases
rate.
2*
The hydraulic gradient increases with decreasing exit weir
th increasing liquid flow
height.
3. The hydraulic
gradient may be predicted by use of a anning-
type friction expression.
4.
The hydraulic gradient on a perforated plate is about 17%
of that on a bubble-cap plate operating at the same liquid
rate per unit of plate width and the same exit weir height.
2
5, The pressure drop through the perforations for both a dry
plate and wet plate is a function of the square of the vapor
velocity,
6, The total plate pressure drop increases with increasing vapor
velocity.
7? The total plate pressure drop increases with increasing liquid
rate,
8, The total plate pressure drop increases with increasing exit
weir height,
9,b nowing the vapor velocity through the perforations,
weir
height, and liquid flowrate, the total plate pressure drop
may be calculated
by use of the equation:
= - h t ht + 046 h,
10o The total plate pressure drop on a perforated
plate is about
92%of that on a bubble-cap plate operating at the same
vapor rate per unit area of plate, the sameliquid rate per
unit of plate width, andthe sameliquid level on the plate.
If the samecomparisonis madewith the plates operating at
equal seals (liquid level on the perforated plate equal to
the height of liquid above cap slots of thebubble-cap plate),
the perforated plate drop is about 68%of that on the bubblecap plate.
The hydraulic gradient data were correlated very well by the use
of a anning-type friction expression:
ft Vf2 N
2grh
Where f' was correlated against Ret:
Re"
This correlation
gradient
rh,'7fp
was used to develop a method forpredicting
hydraulic
on a perforated plate hich
height and the liquid rate,
depends only upon the exit weir
The plate pressure drop on a perforated plate was correlated with
the expression:
ho = OVp2
With a perfectly dry plate, the constant was found to be 0o00029,
However, with liquid on the plate, the pressure drop through the
perforations was greater than predicted using this constant, and the
constant 0.00047 was found to apply,
The higher pressure drop was
believed to be a result of regions of inactive perforations present
during stable runs,
The total plate pressure drop was found to consist
of the above-mentioneddrop through the perforations, a loss due to
surface tension effects,
and a loss equivalent to the hydrostatic hea.
of the liquid above the perforations,
A procedure was developed for
predicting the total plate pressure drop on a perforated plate in the
studied,This procedure depends only upon the
range of variables
vapor rate, liquid rate, and exit weir height.
4
II INTRODUCTION
A. Object of the Investigation
This thesis has two main objectives:
1. To develop a simple method of predicting
pressure drop on
a perforated plate.
2.
To present a practical
method of predicting
hydraulic
gradient on a perforated plate.
At the present time perforated plates are used to a limited
extent in fractionating columns as a means for promoting vapor-liquid
contact,
Their simplicity of construction makes the cost of both
fabrication and maintenance low in comparison to that of the commonly
employed bubble-cap plates.
They have proven effective
for liquids
containing suspended solids, such as the beer mashes in alcohol
production, which tend to clog bubble-caps
The chief objection to the use of perforated plates is their
tendency to t'dump"or "prime" more easily than bubble-cap plates so
that they operate satisfactorily
liquid
within a narrower range of vaporand
rates,
The successful operation of a perforated plate depends to
large
extent on the pressure drop of the vapor in passing
a
through
the
plate and on the hydraulic gradient of the liquid passing over the
plate,
As the vapor flow rate in a column is increased, the pressure
drop per plate increases until it reaches the point where liquid can
no longer flow dom
the dovnpipes and may even begin to flow upward,
resulting in "priming."
As the liquid flow rate is increased in the
tower, liquid flowing across a plate suffers increasing energy losses
due to flow friction, resulting in increased hydraulic gradient.
Particularly in columnsof large diameter, a liquid flow rate is
finally reached where the gradient is large enough to prevent the flow
of vapor through the perforations at the upstream end of the plate.
On further increasing liquid flow rate, the liquid at the upstream
end of the plate may actually
dump"through the perforations so that
the plate is by-passed by a portion of the liquid stream.
Bubble-cap plates also experience the phenomenaof dumping'
and priming." The caps are constructed, however, so that they will
function properly over a wider range of vapor and liquid rates than
the perforated plates.
At the present time there is little
information available in
the literature whichis of value in predicting either pressure drop
or hydraulic gradient for a perforated plate. It is hopedthat this
thesis will be a substantial contribution for makingsuch predictions.
B. Limitations of the Investigation
All data in this investigation were taken for an air-water
system. In general, maxim
superficial air velocity was 7 ft.
per
sec., while the maximum water flow rate was 24 gpm per ft. of plate
width.
Data for higher water rates could not- be taken since the
plate operation becameunstable at higher rates with the air velocities
attainable.
mercially,
While these rates are not the maximumrates used eom.
it is believed that the rates do cover the ranges ordinarily
encountered. The minimumsuperficial air velocity included in this
investigation was 5.7 ft. per sec., since at lower air velocities the
plate became unstable.
The minimnu water flow rate was zero.
8
The maximumexit weir height for standard operation was 1 inch.
With higher weirs, it was found impossible to operate the plate stably
at the air velocities attainable with the apparatus.
The limiting factor for maximum
weir heights and liquid rates was
found to be the capacity of the air blower. By covering one-half to
three-quarters of the perforated area, the maximum
superficial air
velocity
was increased to about 25 ft. per see., while the maximum
water rate was increased to about 90 gpa per ft. of plate width.
With
three-quarters of the perforated plate covered, the plate operation
was observed
to be promising at a superficial air velocity of about
20 ft. per sec. with a seal of about 5 inches of clear water.
With one-half of the plate covered, some quantitativedata were
taken using a 1 1/2" exit weir. The superficial air velocity in this
case was about 12 ft. per see., while the water rate was varied from
no flow to about 50 gpm/ft. Some qualitative
observations
at this air velocity using a 1" exit weir. Starting with
rate, the operation was stable.
was reached
were made
a low water
Increasing the water rate, a point
where the plate was unstable (approximately40 g/ft.).
In this region of operation, masses of foam moved back and forth
diagonally across the plate giving a "washing machine action."
action "dumped"large quantities of water through the plate.
This
As the
water rate was increased, the above action gradually disappeared until
the plate was operating with fair stability at a water rate of about
65 gpm/nft
The high velocity of the water across the plate evidently
allowed no chance for these oscillations to take place.
With further
increase in water rate, the stability continued to improve
until
the
7
operation of the plate,
at a water rate of about 90 gpm/ft., appeared
to be as good as, if not superior to, the operation at any other range
of water rate.
In conclusion, the ranges of water and air rates used are considered to be representative of those which might be encountered in
industry.
0.
Terminology
ry Plate - A perforated plate with no liquid on it, i.e.,
completely dry.
Dmping
- The action of a plate when liquid flows down through
the perforations so that the plate is by-passed by a
portion of the liquid.
Hdraulic
Gradient ({Ah)
The
two points on a plate.
difference in head between any
Tiless otherwise stated, the
difference in head betweenthe inlet calmingsection and
the outlet calming section.
Hydrostatic Head- (h) - The pressure exerted at any point in the
liquid by the liquid above. Unless otherwise stated, the
pressure exerted on the plate at any point along its
length by the liquid above.
Instability - A plate is considered unstable when the quantity
of water passing down through the perforations becomes
area.
greater than 0.2 gpm/ft*2 of perforated
Piming
- If the level of the liquid at the upstream
side
of
plate plus the height of the liquid columnwithin the
the
8
downspout, equivalent to the pressure drop between plates,
exceeds the height of the downspout, liquidwillbackup
the downspoutto the plate above. This action is referred
to as priming.
Seal
-
of clear liquid present on the plate,
The height
Unless
stated, the hydrostatic head at the downstream
otherwise
calming section expressed in inches of
Su erficial Air Velocity - The air velocity
clear liquid.
based
of the bubbling section expressed in ft.
on the area
per seea
Since
data of this investigation were limited to regions of
stable operation, the area of
the bubbling section was
4.17 square feet
TotalPlate Pressure Drop (hT)
-The
difference in pressure
between the vapor in the space below the plate and the
vapor above the liquid on the plate.
A perforated plate with liquid, either standing on
Wet Plate
it or flowing across it.
D.
Previous Work
Previous investigations of hydraulic gradient have been confined
largely to bubble-cap plates.
Klein
(6)
using
The most recent work was carried out by
an air-water system,
He was able to correlate success-
fullythe hydraulic gradient on a bubble-cap plate with operational
variables by the use of a anning-type friction expression.
His
conclusion was that the hydraulic gradient on a plate is a result of
the frictional losses suffered by the liquid in
platse
It
has
been found
flowing across the
that frictional drag is much higher for
9
aerated than for non-aerated flow. The energy lost as a result of
friction is compensatedby a loss of hydrostatic head whichproduces
the hydraulic gradient.
lein found that the hydraulic gradient
increases with increased liquid rate, increases slightly with increased
air rate up to the point of complete aeration, and decreases with
increased skirt clearance, seal, and weir height. Basedon the
gradient correlation, a relatively simple design procedure for the
of hydraulic gradient was developed depending only upon
prediction
the exit weir height and the liquid rate.
The operation of perforated plate columnshas been investigated
by Eirschbaum().* He found that perforated plate efficiency, general
conditions being equal, is superior to that of a cap-type plate.
With
efficiency
drops off rapidly because of
decreasing vapor velocity,
withplate
liquid dripping through the plate ("dumping")* In columns
spacing great enough to prevent entrainment from becoming an important
factor, enrichment increases as vapor velocity increases until the
optimum load is exceeded. It then decreases evenly because of
decreased vapor-liquid contact time. At excessive vapor velocity,
the
perforated plate pressure drop is so excessive as to cause "priming."
Kirstbaua mentions also that the capacity of perforated plates to
carry low vapor loads diminishes as plate diameter increases, while
the upper load limit,
imposed by priming," stays almost constant.
Plates of larger diameters also exhibit better efficiencies in their
operating range.
Kirschbaumattributes
the pressure drop of the vapor between
plates to twotypes of losses; a static loss due to the head of liquid
10
on the plate, and a streaming loss whichis analogousto fluid flow
through an orifice and is a function of the square of the superficial
The pressure drops encountered by Eirschbaum may have
vapor velocity.
been excessive because he employedplates with small perforations on
relatively large centers.
used by him had
A representative plate
B25 rm4 holes on 9 mm equilateral
triangular
centers.
Kirschbaum also investigated increasing efficiency by employing
atomizing effects on perforated plates using no exit uwir. He found
that the atomizing effect was not sufficiently perfect to obtain
comparableto that which can be realized
rectification
layer using a weir.
He also tested a orrugated
the sides of the corrugations.
with the foam
plate with holes in
With this plate and no weir, he
obtained a cross-current, atomizing effect between liquid and vapor.
The results proved no better.
Kirsehbaum's work is valuable from a qualitative point of view
because he tested various modifications of the perforated plate.
By varying perforation diameter and pitch, he obtained varying amounts
of vapor passage
area.
Increasing
the
area of vapor passage decreased
the plate pressure drop but did not remove the dependence of the
pressure drop on the square of the vapor velocity.
small
a ratio
of pitch
He found that too
to diameter for the perforations led to merging
of vapor streams above the holes and, therefore, loss in efficiency of
vapor-liquid
ontact.
However, Kirschbaum attempted no quantitative
correlation of hydraulic gradient andpressure dropwith vapor and
liquid loading.
The perforations on a perforated plate function as submerged
orificese. Mcoldrick
(7) attempted a correlation of the pressure drop
11
through a single submerged orifice with vapor velocity and liquid head
above the orifice.
Using various liquids and air as a vapor, he found
that the pressure drop throughan 1/8 in. orifice
and liquid
above was
affected by the liquid height, air rate, liquid surface tension, and
liquid density.
water
He proposed the following correlation
for
an air-
systema
Pw a 0.003
Where
()2+
H h. x
P
total pressure drop in inches of water.
q
rateof airflow in cubic feet per hour
volumetric
through the 1/8 in. orifice.
Hh m Hydrostatichead in inches
of water.
Correction factor due to surface tension*
X
This correlation indicates that
the pressure drop corrected
for
hydrostatic head is essentially that of air through a dry orifice.
the surface tension corrections to be small in
McGoldrickfound
comparisonto the other factors and essentially constant. However,
at high vapor rates, the air funnels through the liquid and the
surface tension factor becomes negligible.
The dry orifice loss is
similar to that predicted by Kirschbaum().
McGoldrick fails to present a general correlation for the
pressure drop through a submerged orifice, since his equation involved
the experimental factor LX Robinson and Gilliland (),
h6wsver,
suggest the following equation for the pressure drop through the
perforations:
Whexe
r
pressure dropthrough perforations,
inches of liquid.
I m surface tension, dynes per oni
Pr 2 vapor density, lb. per ou, ft.
/2 * liquid density, lb. per ou. ft.
=--velocity based on total perforation
S m diameter of
area, ft. per sec.
perforation, in,
Kirschbaumxand Andrews ()
have found that incorrect
leveling
produces unevenliquid distribution to a greater degree with perforated
plates than with bubble-cap plates.
With low vapor velocities,
impossible to arrange conditions so that equal distribution
it was
of vapor
flow was maintained over the whole surface of the plate, although the
plate could be precisely leveled with adjusting screws.
Gunness and Baker ()
made etensive
tests on a 5 1/2 ft.
diamater
beer still being used to separate alcohol from a beer mash. Perforated
plates with 1/2 in. holes on 1 1/8 in. equilateral triangular centers
ware employed at 18 in. spacings in the column.
perforations.
ach plate had 2,500
Rates of flow and pressure drops over each plate were
measured. The column operated at a feed rate of 720 lbo/min. and a
steam rate of 162 lb./min. Pressure drops per plate averagedbetween
2 and 3 in. H20 with a vapor velocity of 17 ft./sec.
through the
perforations. The results indicated that the perforated plates gave
efficiencies
lower than those attainable with bubble-eap plates.
The
nature of the mash made use of perforated plates desirable because of
the difficulty involved in cleaning clogged cap plates.
The investi-
gators
made runs Justafter the plate had been cleaned
several
weeks after the column had been in operation. The fact that
and also
13
perforated plates can efficiently handle ontaminating liquids is
borne out by the results,
The most recent quantitative investigation
oncerningbydraulic
gradient on perforated plates was carried out by Hutchinson, Buren
and Miller ( )
The objective of their investigation was to obtain
data which would indicate the type of liquid depth to be used for
hydraulic gradient correlations.
They developeda theoretical
analysis of aerated flow which indicated that the proper depth factor
for correlation was an effective aerated seal (that is, the hydrostatie
head of the foammeasured in terms of clear liquid flowing),
They
correlated their data on this basis.
The investigation was carried out on a stainless steel plate
having 1/8 in. perforations on 3/16 in. equilateral triangular centers
with the long dmension parallel to liquid flow. The perforated area
was 23 in. wide and 47 in. long, the upstream calming section varied
from 16 in. to 30 in.,
and the downstream calming section was 20 in.
long. The length of the aerated section was varied from 47 in. to 30
in. by blanking off the upstream holes, and the width was reduced by
half for high liquid rates (over 2,000 gph/ft.).
were madewith a 1%forward tilt
velocities up to 9 ft./sec.
of the plate.
Three sets of runs
Superficial air
and liquid rates up to 4,000 gph/ft. were
used.
Hutchinson, Buren and Miller found it necessary to consider the
effects of aeration in interpreting fluid flow data on the perforated
plate.
factors:
These effects were included in the correlation by the following
14
deP
i
Aerationfactored _
Density faotor
=iaerated densit
clear density
wherethe subscripts "a"and b" refer to to liquid depths at the
samepoint on the plate under different flow conditions.
dA
P
pressure drop through the plate.
-
clear liquid head on the plate.
;/0 clear liquid density.
They also found that:
1. Hydraulic gradient increased with increased liquid rate.
2* The gradient decreased with increased seal.
35.For a sloped plate, the absolute gradient increased compared
to a flat plate under the same conditions$but the
relative to the sloped plate decreased.
gradient
4. There was a logarithmic variation of gradient with average
seal,.
5. The gradient decreased with decreased length of the aerated
section.
The previous literature appears to lack suitable correlations
of both hydraulic gradient and pressure drop with the variables;
liquid rate, vapor rate, andweir height. The object of this thesis
is to makethese correlations
15
III
PO,DURN
A- Experimental Program
To develop a correlation for the pressure drop on a perforated
plate, it was felt necessary to first investigate the pressure drop
with no liquid on the plate.
hese data led to the conclusion that
the pressure drop was similar to an orifice-type
loss and could be
calculated with the standard orifice equation.
The next step was to see if the pressure drop through the
perforations was similar when liquid was held on the plate.
investigation,
For this
data were taken using various weir heights with a
negligible liquid flow rate to offset leakage at the downstreamweir
and through the perforations.
The hydrostatic head readings in the
bubbling section were averaged and, together with a calculated pressure
loss due to surface tension, subtracted from the total plate pressure
drop. The remaining loss was that due to passage of the air through
the perforations and proved greater than that for a dry plate.
During
the investigation, it was noticed that although the plate was operating
in a stable range, regions of perforations were inactive whenthe
plate was viewed from the underside by means of plastic windowsin the
air chamber. t was reasoned that this phenomenon
was responsible for
the eessive
pressure drop on the wet plate.
The quantity of liquid
leaking through the plate was measured and proved to be alight.
Previous
work with
Fanning friction
hydraulic
gradient
bubble-cap
plates
(6) has shown that a
factor type expression can be used to correlate
data.
To test
its applicability
to a perforated
plate, runs were madevarying liquid and air flow rate and also weir
16
height.
The gradient was measured by subtracting
the downstream
clear liquid level from that upstream. Becauseof the horizontal
direction in which air was led to the air chamberbelowthe plate,
the air leaving the perforations had a velocity vector in the downThis tended to raise the level in the downstream
stream direction,
calming
section above that in the upstream calming section, giving a
reverse hydraulic gradient effect
when no liquid was flowing. Several
runs were made to measure this effect at various air rates and liquid
seals with no liquid flow and a plot of correction values was developed.
These corrections were applied to the hydraulic gradients measured
during liquid flow runs to make them equivalent to gradients measured
on a plate
ith vertical air flow to the perforations.
Applying the sanning-typefriction
factor
expression
to the
hydraulic gradient data as a method of correlationyielded results
that
were quite
satisfactory.
To investigate plate operation at high air velocities, it was
necessary to blank off the upstream half of the perforated area.
Because the air vector effect mentioned above was more pronounced and
errors involved in measuring hydraulic gradient doubled, the data
taken at high air velocity and high liquid seal proved unsatisfactory.
However,
the runs served in obtaining qualitative information regard-
ing plate operation.
B.
Description of Apparatus
The
apparatus
by Ghormley ()
used
in this thesis was adapted from that constructed
and Seuren (
and more recently used by Klein ().
The
17
apparatus was originally constructed and used for the investigation
of the operating characteristics of bubble-capplates.
The apparatus consisted of an air-tight
covered
2-EP.
by the
perforated
Gould centrifugal
measuring devices,
chamber which was
plate; a 15-HP. Sturtevant blower; two
pumps; three
55gallon
drums; and various
such as manometers and orifices.
The regionabove
the plate was enclosed so as to allow for liquid flow. The forward
side was constructed of three panes of glass to allow observation of
action on the plate.
T~vplastic windowswere located in the air
chamberenabling observation of the underside of the plate during
operation.
Figure 1 is a schematic representation of the apparatus.
blower was Joined to the air-tight
The
chamber by means of an 8-inch
duct, makingit possible to force air through the perforated plate.
The maximumair capacity was 2,000 fmtagainst atmospheric pressure.
The air rate was regulated by means of a slide damperin the blower
discharge
line
and was measured by means of an orifice.
later was pumpedover the perforated plate from the three drums,
which were oined in parallel,
by the two centrifugal
pumps connected
in parallel having a maximumcapacity of 140gpm. The water rate was
controlled by a globe valve in the 2-inch water line leading from the
pumps to the upstream end of the perforated plate and was measured
by an orifice.
An inlet weir was used to insure even distribution
the water flow across the plate section.
of
In succession, the water
flowed through an inlet calming section, over the perforated section
~~~_
of the plate, through an outlet
-
k
l-
--
calming
section, and over an adjustable
18
_
__
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c
w
a
Z4
;o
m
,;c
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1118--
i.
_ ___
outlet weir to the surge drums completing the cycle.
The perforated
plate was constructed
by WickwireSpencer, Ic,
from 14 gauge steel sheet
to the following approximate dimensions:
Over-all dimensions
120"
Upstream edge to inlet weir
Length of inlet calming section
Length of perforated section
12"
24"
60"
Widthof perforated
10"
section
Length of outlet calming section
13 1/2"
24"
The perforations were 1/8" diameter on 1/4" equilateral triangular
centers, the long dimension parallel to liquid flow. Figure 2
indicates the location of taps in the plate which allowedmeasurement of the hydrostatic head at various points along the length of
These taps were connected to open-end manometers.
the plate.
in
indicated
Also
igure 2 are the three taps located in the air chamber
for measuring the total plate pressure drop.
These taps were connected
to open-end water manometers.
For the runs in which no liquid was used on the plate, straightening vanes were inserted beneath the plate and perpendicular to the air
flow for better air distribution and to produce a more vertical air
flow through the perforations.
These vanes were removed during runs
with liquid on the plate because they reduced air flow through the
perforations directly above them.
rimental Procedure
C.
The operation of the apparatus was essentially the samefor all
runs in which liquid was used. A typical run is outlined below:
1.
The hydrostatic
head manometer lines were purged of air by
forcingwater throughthem fromthe plate
/
taps.
After this
20
_ _
_
_
-
-
_
-
i
FIGURS
?1P FORAT3D
PL.A,
2
LAYOUT
I
"I I R
w,7E
HYIn
DRO
an90
S,
IA
?R3SUR
DR
TAPS (I,II,
I
II
kF3RATD
SECTION
III
IRH
8 /* -'/
_
_I____
I ~-1----~1w---- - -----
--
I
procedure, the water levels in the manometers should be the
Ii
same and should lie on a horizontal line.
If they did not,
adjustments were made to level the plate by means of leveling
boltson the legs of the apparatus.
(See Appendixfor details
of plate leveling.)
20 The desired exit weir was installedo
3. The air blower was started with the damper fully opened.
4.
The pump (or pumps) was started
and the globe valve in the
water line adjusted for proper flow rate.
5. With the plate covered with water and liquid flowing over the
exit weir, the air damperwas adjusted to give the desired
flow rate.
6. The lines leading to the pressure drop taps were drained of
any water that had collected in them. The taps themselves
were shielded against water droplets from the plate, and
the draining procedure was necessary only during very unstable
plate operation.
7. After about three minutes were allowed to reach steady state,
readings were taken of the hydrostatic head manometers, the
plate pressure drop manometers, the water and air orifice
manometers, the air temperature, the air pressure upstream
of the air orifice, andthe weir height.
D. Method of Correlation
1.
Hydraulic Gradient
The hydraulic gradient data were correlated by a
anning
friction factor type expression by plotting a modified friction
-
_e
22
factor as a function of the Reynolds number,
2.
Pressure
Drop
The pressure drop data were correlated by plotting the air
velocity through the perforations against the pressure drop of
the air passing through the perforations.
With both the dry
and the wet plate, curves were obtained which indicated the
dependence of the pressure drop through the perforations on the
square of the air velocity.
A completedescription of the abovecorrelations is given in the
section
II
titled
DISCUSSION O
RESULTS.
_ __
I
WV
The hydraulic
gradients
RESULTS
measured
on the plate and corrected for
the air velocity vector (see Section III) are shown in Figures
and
4 plotted against the operational variables. In Figure 3 the hydraulic
gradient is plotted against the water rate at various weir heights.
Figure 4 showsthe effect of air rate on the hydraulic gradient at
various weir heights.
It can be seen that increasing water rate and
decreasing weir height both tend to increase the hydraulic gradient,
whereas varying the air rate
has little effect on the gradient.
This
latter feature indicates that operation was in the range of full
(
alein's
aeration and verifies
is independent of vapor velocity.
conclusion that hydraulic gradient
The trend of the 1-inch weir data
in Figure 4 might indicate that aeration was not complete at the low
air rates with this liquid levels
The pressure drop on a dry perforated plate is plotted against
air rate in Figure 5.
logarithmic
The straight line with a slope of tw
on
paper indicates the dependence of the pressure drop on
the square of the air velocity.
The total plate pressure drops are shown in Figures 6 and
plotted
against the operational variables.
Figure 6 is a plot of the
total pressure drop against air rate at various weir heights with
negligible
heights
weir
water
flow.
on the total
The effect
pressure
of the water flow rate at various
drop is illustratedin Figure 7.
The total plate pressure drop can be seen to increase with increasing
air rate, liquid rate, and weir height.
-
-
24
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The hydraulic gradient and pressure dropdata shown in these
Figures were used to develop correlations and methods of prediction
(see
Section
V - DISTU3SI[
OF EStULTS).
The mainresults of this thesis are:
A. A correlation for the hydraulic gradient data.
B. A alculation procedure for predicting hydraulic
gradient.
0. A correlation for the pressure drop data.
D. A calculation procedure for predicting pressure
drop.
30
V
DISCUSSION OF RS1LTS
A. _ydraulic Gradient Correlation
In his investigation of hydraulic gradient on bubble-capplates,
Klein(6) found the gradient to be independent of vapor velocity
reaching the point of full liquid aeration
after
He further found that the
bulk of the hydraulic gradient occurred in the bubbling section and
that the hydraulic gradient data were correlated by meansof a Fanning-
type friction factor
A study of the hydraulic gradient data in Figure 4 for the
perforated plate both indicates that operation was in the region of
full aeration and verifies Klein's conclusion that hydraulic gradient
is independentof vapor velocity
The flow of liquid across a perforated plate is essentially the
same as that across a bubble-cap plate.
In each case there is a
constancy of liquid or foam velocity and area available for flow
It
seemed reasonable, therefore, to assume that the bulk of the gradient
muld occur in the bubbling section of the perforated plate and that
the hydraulic gradient data muld
be correlated by a Fanning-type
friction factor,
The hydraulic gradient data were used to calculate a modified
friction factor from the expression.:
F a f' Vf 2 N
2gc rh
Where
F -
nergy loss across the bubbling section
h = hydraulic gradient (in. of H20).
()
24
h (ft.of HpO).
Pf
I
Vf
W velocity of foam (ft/sec.),
N
m
length of bubbling section (ft.),
gravitational constant (ft./sec. 2 ),
c
rh
modified friction factor,
=
hydraulic radius (ft.).,
The hydraulic radius was obtained from the equation:
rh
WJhere
b
m
Lc -
(2)
bL
channel width (ft.).
calculated foam height
hydrostatic head (ft.)
twice the downstream
(6),
The foam velocity was calculated from the equation:
G
Vf
(3)
(60) 7-46L'
Where
G'
liquid flow rate (gpm/ft. plate width),
Q+=
fractional volume of the foam occupied by the
liquid
= 1/3 (.
The modified friction factor was plotted as a function of the
Reynolds number of the foam which was obtained from the equation:
Ret
Where
Re'
_
rh v Pf
4
Reynolds number of foaMn
:f
.- effective foam viscosity (lb./fto-sec.)*
/O
::s effective foam density (b/ft.
The foam density,/4
3
),
, is essentially the weight of liquid
contained in a unit volume of foam.
Since
is defined as the
I
fractional volume of foam occupied by the liquid, it follows that
may be calculated
from the expression:
P Pi
/M
1
Where
(5)
density of the clear liquid (lb./ft.3).
There being no simple, accurate expression for calculating foam
amounts of air and water in the foam, a
viscosity from the relative
similar
expression was used for oalculating
f:
Af:Af
Where
1
(6)
clear liquid viscosity.
Any error introduced by use of the above equation affects the correla-
tion only by shifting the plot of the friction factor, f', along the
Re' axis.
)Figure8 showsthe modified friction factor, f', plotted vs.
the Reynolds number for various weir heights.
The points for each
weir height are seen to lie on a straight line.
As the weir height
and, consequently, the seal increases, the friction factor for a given
Reynolds number increases.
It would be convenient to draw the lines for the various weir
heights into a single line.
Since f' and Re' are dimensionless, the
factor
used to draw the lines of Iigure 8 together should
be dimension-
less.
Several factors were tried, andthe factor T was chosen:
(57)
he - Dp
Where
Dp
diameter of the perforations (in.).
he =-dowastream hydrostatic
head (in. of H2 0).
33
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Pr
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6
7
34
This factor was employedwithout a theoretical basis and maynot apply
on a plate with a different perforation diameter or perforation
The plot
pattern
of
'T vs. aRe is shown in Figure 9.
xcluding
the data for the 1 1/2" weir, this plot is seen to correlate the data
quite well.
Since it was found impossible to obtain data for weirs
above
" at the vapor velocities attainable with the aparatus,
of
perforated
the
half
section was covered in order to obtain the data for
the 1 1/2" weir. For all weir heights, it was found necessary to
correct the hydraulic gradient data for the velocity vector of the
air (see section III).
This correction was made for the 1 1/2" weir
data and the gradient then doubled so as to correspond to a five foot
Therefore,
bubbling section as in the case of the other weir heights.
any error in either the data itself or in the correction for the air
velocity vector was doubled. Since all points for the 1 1/2" weir
data lie on the "high" side of the line, it is felt by the authors
that the correction for the air velocity vector was in error.It is
interesting to note that all points for the 1 1/2" weir data lie along
a line parallel to the original line if one point
is excluded.
In summingup the above discussion, it was found that hydraulic
gradient for the perforated plate could be predicted by use of a
modified
anning equation.
The modified Fanning friction
various weir heights were found to be correlated
Re.
factors
by plotting
for
f' x T vs.
Of noteworthy interest is the fact that the modified Fanning
friction factor for the perforated plate is about 17%of the same
factor for bubble-cap plates with the sameweir height and operating
at equal Reynolds numbers (6).
A comparison of hydraulic gradient data
35
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36
for
the two types of plates operating with the same water
rate
and
weir height verifies the fact that hydraulic gradient on the perforated
plate is about 17% of that on a bubble-cap plate*
B. Calculation
Procedure
forPredictirng Hydraulic Gradient
On the basis of this investigation, a procedure is
offered
for
calculating hydraulic gradient on a perforated plate operating uGer
stable conditions knowingthe liquid flow rate across the plate, the
exit weir height, ad assuming complete aeration.
l1 The dovmstream
clear liquid level, h , is determined from
the liquid flow rate and the exit weir height by use of the
standard weir equation.
2.
The foam height,
L,
is twice the downstreamhydrostatic
head:
Lo
2h
3 12
3,
(ft.)
/f,
The effective foam density,
is calculated from the
expression:
3
- p1(lb./ft.
/9£
4,
The value of
radius,
L
)
()
is used to determine the hydraulic
r , and the foam velocity, Vf :
rh
bL c
bL
( ft.)
b + 2LE
vf
(ft./sec)
G=
60 /f
(2)
(3)
Lc
5, The effective foam viscosity,
,, is calculated
from the
expression:
f,C/c ]
(lb/f.se.) (6)
37
6.The Reynolds numberof the foam, Ret , is obtained from the
equation:
4)
r,=rh V(
7.
8.
nlowingRet, ft is obtained from Figure 8.
The hydraulic gradient, A h, is determined from the modified
Flaning equation:
f
Z1
Wlhere
Vf2 N
2 g rh
h - 24
(in. of liquid).
C. Pressure Drop Correlation
The drop in pressure of air passing through a perforated plate
with no liquid on it was found to be a function of the square of the
air velocity and could be represented by the equation:
ho
lhere
(8)
Vp2
ho - pressure drop through perforations (in. of H20),
Vp
O
air velocity through perforations (ft./sec.).
eperinental
constant
000029.
This is the equation of the straight line in ligure 5, obtained by
plotting on logarithmic paper the velocity of air through the perforations vs. the pressure drop across the plate.
In order to obtain an
equation applicable to vapors other than air, Equation 8 maybe converted to the more general standard orifice equation:
2VC
ao
/P
(9)
38
Where
Vp
vapor velocity
through perforations
(ft./sec.).
ho _ pressure drop through perforations (in. of liquid).
liquid density (lb./ft.3).
?01
/Pv - vapor density (lb./ft.S).
/34
WhereA. is the hole area (ft. 2) and
As is the perforated section area (ft. 2 ).
2
LAaj
experimental constant.
0
The experimental constant was found to be 0,86.It is believed that
this high constant obtained with a dry plate can be accounted for by
reasoning that the air streams leaving adjacent perforations interact
and flow characteristics
a single orifice.
result which differ from those peculiar to
The tendency is for the pressure drop to be less
air velocity,
than for a single orifice at the s
Equation
with
employed
usually
The constants
9 for a single orifice range from
0.60 to 0.80.
The drop
in pressure of air passing through
with liquidon it was found to consist
1.
type
An orifice
a perforated plate
of the followingcomponents:
loss which could
not be calculatedusing
Equation 8,
2. A loss due to surface tension effects.
3.
A loss equivalent to the hydrostatic head of the liquid
above the perforations.
Orifice tpe
loss.
By subtracting
the
surface tension effect and the
hydrostatic head loss from the total plate pressure drop and plotting
the remaining plate pressure drop on logarithmic paper against the
39
air velocity, a straight line with a slope of two was obtained.
in Figure 10. The equation of this line is:
is illustrated
ho =
Where
This
2
(lo)
ho - pressure drop through perforations (in. of HE0)
Vp = air velocity through perforations (t/sec),
0
=
experimental
constant
0*00047
t
At equivalent air velocities (based on total area of perforations,
Ap),the pressure drop of the air passing through the perforations was
found greater for the wet plate than for the dry plate.
that this was caused by partial inactivity
It is believed
of the perforated area
which is attributed to the wave otion of
tion
o the
the bubbling liquid on the
plate.
Since the velocities were calculated from the volumetric air
rate to the plate and the total hole area, they did not represent the
actual velocity in the case of the wet plate with its inactive regionso
Assuming that the pressure drop on the wet plate should be the sa
that on a dry plate, Equation S was used to calculse
a velocity
as
from
the pressure drop. It was found that about 20%of the perforated area
had to be unavailable for air flow during a stable run to cause the
higher pressure drop. This agreed with an estimate of 25%inactivity
made by viewing the underside of the plae through plastic windows
during operation,
Although about 20%of the perforations
were estimated to be
inactive during a stable run, this portion of the plate was not
dumping.
Regions of high hydrostatic head seemedto moveacross the
plate in the direction of liquid flow causing the perforations underneath to be inactive.
However,the actual leakage caused by this
40
IC
:--"' :"
: :
B
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7
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5
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2
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+..,
1
15
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Ir
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::
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::;
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S
4
S
8
20
30
40
50
60
Air Velocity - Vp (ft./sec.)
4
· 1· t '·
:,
l....i..
i· ·
'.
·
--
t.......
Ji :
-·-
..
"
,
'--i·--~,,
::::::::::::::::::
~~~~~_
tt--,---- ·--
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. .~.' ;
,
-,-?'"
i~·
.
'
7
70
a
80
WPT
&
·1
9
!·
10
90 100
41
was very slight during stable runs, amunting
phnono
to approxi-
mately 0.015 gpa/ft. 2 perforated areao
At higher air velocities than could be obtained with the exist-
ing apparatus, it is believed that the inactive areas would gradually
disappear and the plate pressure drop would then follow Equation 8.
Converting Squation 10 into the more general standard orifice
equation, Eiquation 9, yields an experimental constant of Oe68. This
constant obtained with a wet plate is more in line with constants
usually encountered for use in quation 9. However, it is believed
that the velocity used to calculate the constant in this equation, Vp
:1
is not the actual velocity on the wet plate as explained above,
An alternative explanation for the constant, 068, would be
that although regions of inactivity were observed from the underside
of the plate, the estimate of 20%inactivity mayhave been too high
and actually most of the area was active,
If this were true, the
velocity used to calculate the constant would have been correct,
It
is suggested that the clear liquid layer below the foam and ext to
the plate greatly reduces the interaction of air streams from adjacent
perforations, and flow is more nearly like that through a single
I
orifice.
This would explain the
fact
that
the. more
normal constant
of 0.68 applied rather than 0,86 which was found to apply with the
dry plate.
Surface tension loss.
To account for the loss in pressure due to
surface tension effects, the following equation for the formation
42
of bubble surface was applied:
0.04 Y
t
Where
/
D
()11
ht = pressure drop due to surface tension effects
(in. of liquid).
liquid surface tension(dynes/cm.).
3DP
perforation diameter (in.).
This lossamounted
to 037 inchesof water for the system studied.
McGoldrick (
found this equation to apply for a single 1/8-inch
orifice and for air velocities similar to those encountered in this
thesis.
The equation was, therefore, employed and proved satisfactory
in correlating the pressure drop data
Hydrostatic head loss.
The pressure to be overcomeby the air leaving
the perforations is equivalent to the hydrostatic head of the liquid
above the perforations.
plate was found to
The hydrostatic head profile for
be similar to that encountered with
a perforated
a bubble-cap
plate (6}) A region of low hydrostatic head was formed in the bubbling
section.It was found that with weirsup to one inch and air velocities
(through the perforations) up to 30 feet per second, the averase
hydrostatic head in the bubbling section was
p
mroimately0.46 times
that in the downstream calming section.
Comparing data taken by Seuren (9) of the total pressure drop on
a bubble-cap plate with the total pressure drop on a perforated plate
operating
at
the
same volumetric
air
rate and water level on the plate
reveals the perforated plate drop to be the lower of the two. Seuren
S
used thirty
aps distributed in an area equivalent to the perforated
area used in this thesis.
level
of 232
At an air rate of 34 ofma/capad
in. on the plate with no liquid flow,
Seuren
a liquid
measured
a total plate pressure drop of 3.10in. of H20o With the same rate
of air to the perforated plate, i.e.,
1020 cfm, and the same liquid
level, a total plate pressure drop of 2.85 in. of HO0was calculatedo
This is about 92%of the drop on the bubble-cap plate.
The height of
liquid above the slots on Seuren's plate was 1.57in
With this same
liquid seal on a perforated plate, the pressure drop vmuld be 2.10 in.
of HI20
or 68%of the bubble-cap plate drop,
D, Pressure Drop Calculation Procedure
The vapor velocity through the perforations, the liquid rate
and the downstream weir height are sufficient data to predict the
total plate pressure drop with the following equation:
h,
he
Where
.
= h o t ht +- 94 6 h
(12)
hydrostatic head of the clear liquid in the downstream
calming section, calculated with the standard weir
formula (in. of liquid),
The value for h o is calculated from Equation 9 using the constant 0,68.
The surface tension effect, ht, is calculated by using Equation ll.
Although Figure 10 was developed using data for 1/4, l/2, 3/4
1,
and 1 1/4 inch weirs, with no liquid flow, the validity of extending
its use to somewhat higher seals vith liquid flow is verified in
Table A IV, where calculated and experimental pressure drops are
compared.
However, it is not recommended that this plot be used for
high seals or for liquids with properties differing widely from water
44
At higher water rates it is to be noted that the calculated drop becomea
I
increasingly lower than the experimental drop. This is partially
explained by the fact that the hydraulic gradient on the plate
auses
a fringe of the upstreamperforations to ease bubbling and in effect
reduees the plate hole area.
The plot was developed from data with no
liquid flow and hence does not include this effect.
Whenthe pressure
drop is calculated using air velocities corrected for this iactive
area, better agreement is obtained between the values of experimental
and calculated pressure drop. This is illustrated
in Table A AI.
45
VI
COONCLUSIONS
The conclusions to be drawn from this investigation of hydraulic
gradient and pressure drop on a perforated plate are as follows:
1o
The hydraulic gradient increases with increasing liquid
liquid flow rate.
2,
The hydraulic gradient increases with decreasing exit weir
height o
3,
The hydraulic gradient may be predicted by use of the Fanningtype friction expression:
F
Where
_
_
_______
f't for various weir heights is plotted versus Re':
Re'
11
_
'
rhvf
f
i
ii
4.
I
vs. Ret for various weir heights may be
The curves of
brought together into a single curve by plotting f'T vs. Re',
where:
I
T Dp
h c - Dp
This correlation is knomw to be valid only for the data of
this investigation. Further study would be necessary to
determine whether or not the correlating factor, , is
applicable to plates of different perforation size or
pattern and to systems other than air-water,
5,
The hydraulic gradient on a perforated plate is about 17%
of that on a bubble-cap plate operating at the same liquid
rate per unit of plate width and the same exit weir height.
6,
The pressure drop of vapor passing through the perforations
of either a wet or dry plate is a function of the square of
the vapor velocity.
7.
The pressure drop on a dry perforated plate is lower than
the pressure drop through the perforations on a wet plate
when operating at equal superficial air velocities.
46
8.
The total plate pressure drop increases with increasing
vapor velocityo
9.
The total plate pressure drop increases with increasing
liquid rate and increasing exit weir height.
10.
Kowing the vapor velocity through the perforations, exit
weir height, and liquid flow rate, the total plate pressure
drop may be calculated by use of the equation:
h0-+ ht+
haW
Where
ho
may be calculated from the orifice equation:
6 (1l
with
e
046
C = 0,68,
ht
4P
may be calculated from the equation:
0.04r
t
11.
D-
At the same superficial air velocity, liquid rate per unit
of plate width, and liquid depth, the total plate pressure
drop through the perforated plate was found to be 92% of
that through a bubble-cap plate. Making the same omparison
with equal seals (liquid level on perforated plate equal
to height of liquid above cap slots on the bubble-cap
the total plate pressure drop through the perforated
plate),
plate was found to be 68% of that
through
a bubble-cap
plate (9),
of a perforated plate in operaheadprofile
12. Thehydrostatic
plate()s
tion is very similar to that of a bubble-cap
13, In the range
perforations
of stable operation, leakage down through the
was found negligible.
The following recommendationsare made for future investigation
of hydraulic gradient a-adpressure drop on perforated plates:
1. Investigate validity of applying the correlations madein
this thesis to lates of different perforation patterns
and with larger perforations.
The factor, T, used in
correlating f' vs. Re for various weir heights would be
3
of particular interest.
2, Investigate validity of applying the correlations madein
this thess
.i
ts plates operating with higher sealsand
greater liquid flow rates by adapting the apparatus to
deliver greater vapor velocities.
3, Investigate validity of applying the correlations made in
this thesis to plates using liquids andvapors with
properties
rrom the air-water
different
system used,
48
I
i
VIII
s
IE4,
APPEDIX
49
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65
A. Sle
Calculations
Sample calculations will be arried through for t
types of
alculations:
1
radient Correlation
Hydraulic
2, Pressure Drop Correlation
1, Hydraulic Gradient Correlation
Data from Run E-2 are used for the
alculations
21 ga rh
Z
ft
vf
Where
(1)
N
= 0.22 =
Ah
24
00092
24
o
= 32.2 ft./sec,
=
i
=b+2I
U f
L
b
= 1, 125 ft.
2
bL
I,
2he
followings
=
12
(2)
l.22)
12
0,203 ft.
rh
=1.125 0203)
m
1.125 + 2(o.203)
= 0.149 ft.
(60) (7,46) Lcf
(60) (7,46) (0.203) (1/3)
5.
plt
=
0 t.
(j2) (.0-92)
(o0516)2
= 00663
32,2) (0,149)
(5.o)
(3)
0.516ft./see.
h - D
0,12
1.22 - 0.12
-
f'T -
0.109
0.00723
rh f Pf
~f p
62,4
=
3
Af
i(5)
3
20.8 lb,it.
1
(6)
0,000672
t
0.000224
o
lb. /ft-se,.
3
t
_ (0,.149) (0,516)
Re(0.000224)
(20.8)
7,14 x 03
2, Pressure Drop Correlation
Data from Run E-2 are used in the following calculations:
VP
X P,
A~Pa
vp - 27,4 x 42_3
P
0,936 x 407
-Vp= 30,5 ft,/seco
=
0.0o Y
P01
=0,04
(11)
P
72,8
62.4 x 0125
67
nt
= 0.37 in. H20
hf
= ho+ ht + hay
h
1
ho
(12)
- 0.37 - o.57
= 044 in. E20 (experimental plate
pressure drop)
ho ,=a VP
o
(10)
o.o000047 (30.5)2
ho = 0.44 in.
20 (calculated plate
pressure drop)
B, Plate Leveling Procedure
The following procedure was employedto insure proper leveling
of the perforated plate and zeroing of the manometerchart:
1. Hydrostatic head manometerlines to the taps in the inlet
and exit calming sections were purged of air by forcing
water through them from the taps.
2. Theperforated area of the plate was blanked off with a
piece of sheet metal.
3.
An exit weir was installed
and water run onto the plate.
Water flow was adjusted to be just sufficient
weir level.
to maintain
If leakage under the sheet metal was excessive,
air was admitted to the air chamberto build up pressure
and stop the leakage.
4.
The liquid levels
in the upstream and downstream calming
sections were measured on the plate and if found unequal,
the plate level was adjusted by leveling screws on the legs
of the apparatus.
68
5* The manometer sheet was adjusted so that the manometers for
the upstream and downstreamcalming sections both read the
same, the reading being that measured on the plate.
Using this procedure, the plate ends could be leveled to within plus
or minus 1 mm#
*. Calibration of Flomesters
1.
Water Rate Measurement
The orifice in the water line was calibrated by direct
measurement. The globe valve in the water line was set, the
system was allowed to cometo equilibrium, and the water orifice
manometerrecorded while water was collected for a measured time
interval.
The water collected was weighed and the water rate
calculated in gallons per minute. This procedure was repeated
for various flow rates andthe results plotted to obtain a
curve of water rate vs. the water orifice manometerreading.
2.
Air Rate Measurement
Pitot tube traverses were madeacross the air duct for
several air rates.
rom these traverses, the air rates were
determined by means of graphical
integration.
The results
were
used to check the validity of using the standard orifice equation
for non-compressible flow. The use of this equation was found to
be satisfactory
using the experimental constant:
C =
00o6
A curve of air rate, in cubic feet per sec., vs. the air
rate manometerreading was plotted using the orifice equation.
D, Nomenclature
AP=
Total perforation area (ft.2 )
A8
Area of perforated section (t,
),
- Platewidth (ft),
b
Dp
2
-
F -
Perforation diameter (in.).
riction head loss
A h
Modified frictionfactor -
V
(ft. of liquid).
24
2g
rh Z
Vf
~G
=
g
Volumetric flow rate (gpm/ft, of plate width)
Gravitational
A h
N
constant (32,2 ft. lbs. mass/see, 2
lbs. force),
Hydraulic Gradient across plate (in, of liquid),
h
Hydrostatic head (in,
hay
of liquid).
Average hydrostatic head in bubbling section (in, of liquid),
hc
D aownstream
calming section hydrostatic head (in
ho
Pressure drop through perforations (in, of liquid),
ht;
Pressure drop due to surface tension effects (in. of liquid).
hT~
=
Total plate pressure drop (in. of liquid).
La
=
Calculated foam heigh
N
Pa
t
e
of liquid)a
(ft.)h
Length of bubbling section (ft,),
_
Atmospheric pressure (in. of H20),
Ps-
Static pressure upstream of air orifice (in. of H20)
Qe
Volumetric flow rate of air (efm)o
70
rh
Hydraulic radius (ft.),
Re' -
ModifiedReynolds number
orrelation factor
-- _
h c - Dp
T
=
Vf
=
Foam velocity (ft/seec.).
Vp
-
Velocity of vapor based on total hole area (ft./see.),
Factor
r
r
m
rh V
in standard orificeequation.
/3
Surface tension of liquid (dynes/er,).
Foam viscosity (lb./ft. sec.),
Liquid viscosity (lb./ft. sec.),
1
=
3 )
oam density (lb,/ft.
f
/0
Liquid density (lb./ftA,3)
Vapor density (lb,/ft 3 ).
Density factor
effective aerated density
clear liquid- density
A]
71
2.
Literature Citations
1. Ghrmleyt, . L., M.,SThesis, Chem Eng°,MI.T. (1947).
2. Gunaness,R, C., end Baker,
13941400 (1938).
3.
Hutchinson,
. G.,
Ind. n:g. Ohem.,
M. H., Buren, A. G, end Miller,
E3
B. P.,
"Aerated Flow Principal Applied to Sieve Plates,"
unpublished
(1949)
4.
Kirschbaum and Andrews, . Inst. Petroleum Tech.,
803-20, (1936),
5,
Kirschbaum, B., "Distillation
and Rectification,"
Chem. Publishing Co., Inc., New York (1948).
6. Klein,
. H., S.D.
,
264-76,
Thesis, Chem. ng., M.I.T. (1950).
7.
McGo1driok,
8.
Robinson and Gilliland,
"lemsnts
of FractionalDistillation,"
4th Ed,, McGraw-Hill Book o.,,Inc., New York (1950).
9.
Seuren,
10
. E.1,B.S. Thesis, hem. ng., M.I.T. (1950).
. R., M.S. Thesis, Chem.Eng.,M.I.T. (1947).
Weber, H. O.,"Thermodynamics for Chemical Engineers,"
John Wiley & Sons, Inc., New York (1939).