XA04NO014 Measurement of Time Varying Thickness of Liquid Film Flowing with High Speed Gas ...

20 Pages·2012·0.97 MB·English

XA04NO014
Measurement of Time Varying Thickness of Liquid Film Flowing
with High Speed Gas Flow
by a Constant Electric Current Method (CECM)
Toftru UKANO
Department of Mechanical Engineering
Faculty of Engineering, Kyushu University
6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812 Japan
Tel: [phone], Fax: [phone]
E-mail: fukanot(cid:1)mech.kyushu-u.acjp
Abstract
A constant-electric-current method (CECM) developed by the present author is a kind of the
conductance method. The characteristics of the CECM are (1) a constant-curTent power source is
used for supplying the electric power and 2) two kinds of electrodes are installed. One is used for
supplying electric power and the other is for detecting he information of hold-up or film thickness.
The main merits of the CECM are (1) the output from the sensor electrode is independent of the
location of gas phase, for example radial location in a tube cross-section, 2 the sensitivity of
detecting the change in the hold-up is higher in the case of the thinner film thickness, and 3 the
interaction aong the electrodes is negligible. The basic idea, calibration and examples of the
application of the CECM will be discussed in the present paper.
1. INTRODUCT'ION
liquid films flowing with high speed gas flow are widely encountered in various kinds of
industrial equipment It is understood that the characteristics of the liquid films are closely related to
theperfomianoeandthesafeoperationofthoseequipment. hesurfaceoftheliquidfilmisusually
accompanied by various kinds of complicated waves. Therefore the film thickness changes with
time and space. The configuration of the interface depends on the flow conditions of gas and liquid,
which affects the flow pattern, the interfacial shear stress and the breakdown of the liquid film on the
surface as well. And accordingly the acumulation of the information on the liquid film flow is
indispensable.
The change of hold-up is measured by making use of the change of conductance of two-
phase mxture included in the space between a pair of sensor electrodes[l]. If the electrodes are
mounted flush with the surface of the channel, two-phase flow is not disturbed by the electrodes.
In the usual conductance method, however, there are following defects : (1) The smaller the film
thickness, the smaller the output from the sensor electrodes due to the minimized electric current
because usually a constant voltage power source is used, which is inconvenient for measuring time
fluctuating thin film thickness. 2 The distribution of electric current density is not uniform in the
cross-section of the channel especially near the electrodes then the output is dependent on the radial
location of the gas phase in a tube cross section even if the void fraction is the same as shown in
Fig.l. hedetectedvoidfracdoninthecaseofAishigherthanthatofB. (3)Meoutputfromthe
electrodes is saturated if the distance between the sensor electrodes is small compared with the film
thickness, which is a defect for measuring the local value of the film thickness.
The present author developed a new conductance method 2[4), which overcomes the
above mentioned defects of the conventional conductance method, and have successfully applied it in
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many cases of, especially, liquid films flowing wit a igh gas flow. In die present paper the basic
idea, the calibration and the examples of te application will be described.
2. CHARACTERISTICS OF THE CONSTANT ELECTRIC CURRENT MET-HOD CECM)
In Fig. 2 is shown die conceptual drawing of the constant-electric-current method (CECn.
In te CECM die constant electric current is applied from a pair of electrodes, which will be referred
to as the power electrodes in te present paper. The locations of the sensor electrodes for detecting
the time fluctuating old-up are separated from die power electrodes. The distance between the
power electrodes must be considerably large and the sensor electrodes are installed in between the
power electrodes. The axial distance between a pair of sensor electrods is arbitrary, few millimeters
for the measurement of a local value in some cases and several hundreds mllimeters in other cases for
a space averaged value in a considerably long axial length.
Compared with the conventional conductance method the characteristics of the CECM are
as follows
(1) The power electrodes are separated from te sensor electrodes and the distance
between the power electrodes must be much larger than the objective mearsuring section. By this
arrangement of the electrodes the distribution of the electric current density applied by the constant
current power source becomes satisfactory urtiform in the measuring s ection.
Voltage drop is picked-up through a high input-impedance aplifier then the uniform
electric current distribution is not disturbed by the presence of the pair of sensor electrodes. And
accordingly the increase in voltage drop with the increase in the electrical resistance, wich is caused
by the existence of gas phase, is independent of the locations of the gas phase in the cross section of
the duct as shown in Fig. 3. That is, the difference in the output from the sensor electrodes caused
by the difference in the flow pattern i.e., the bubbly flow type and the annular flow type but with the
same void fraction, is smaller in the CECM than that in the conventional conductance method.
(2) In the conventional conductance method the output asymptotically increases with the
increase in the film thickness up to a certain value which is considerably small compared with the
distance between the sensor electrodes. On the other hand in the CECM it is fundamentally
improved, and the distribution of the electric current is uniform independent of the film thickness and
the linearity of the output with the film thickness is quite good.
(3) If the film thickness is very thin, the electric resistance becomes large while the
electric current is kept always constant in the CECM. Then the voltage drop becomes large. The
thinner the liquid film thickness, the larger the output voltage. This means that the sensitivity to the
film thickness variation is higher in the case of the thinner film thickness. Therefore the CECM is
better to be used in the liquid film flow, although the CECM is fundamentally applicable to wider
range of flow pattern as discussed in Figs. I and 3.
(4) Interaction among the sensor electrodes is negligible because the output from each
sensor electrode is measured by a high input-impedance amplifier. herefore multiple sensor
electrodes can be installed at a short distance between each neighboring electrodes in order to
simultaneously measure, for example, the film thickness at many axially different locations.
(5) Even in the case of the simultaneous measurement of the cross-sectionally averaged
hold-up the number of the necessary input power source is one.
(6) Any electrodes are mounted flush with the duct surface and the two-phase flow is not
disturbed by the existence of the electrodes.
3. BASIC EQUATIONS OF THE CECM
The electric resistance of two-phase flow, RTp, in a unit length of the channel is expressed
as follows,
I 1-77 +_ 77
RI-p RG RL
where R. and RL are respectively the electric resistance wen the gas pase and the liquid phase alone
occupies the whole cross-section of the tube, and the hold-up. Express the voltage drop in a
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A B
A B
C)
C) (D
-57-
0 0 1A 0 0
0 0 0 0
<Z:> <-::> CZ:)
0 0 O
Fig. I Distribution of electric current inc onventional conductance method.
Constant current power source
VI
77(cid:1)7
Nonconductive
Duct
Isolation Amplifier
(High input impedance)
Fig.2 Basic idea of the constant electric crrent method (CECK.
A B
VA VB
output voltages in a uniformly distributed electric current in the CECM
I
independent of the location of the gas phase.
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unit length as Vp when a constant current lo is supplied, and the hold-up is expressed by the next
equation if the condition R, >RL is hold as for the case of air-water two-phase flow.
7 = - = (2)
%L =
Io RT,
R7P VT,
here is the voltage drop when the liquid alone flows with occupying die wole cross-section of the
VL
tube. If the electric resistance and the voltage drop are respectively expressed as and V., when
RTm
the hold-up is the known value of and die electric current is te same value as that in the case
of E.(2), 1 , next equation is obtained from Eq.(2),
776 = 10 = (3)
R V
IORTpo
VTpo
By eiminating in Eqs.(2) and 3) the next equation is obtained.
V
77 = 77 = VTPO 77o (4)
IORTPO
10 Rrp
VTP
If VTp is measured under the condition of the known values of and V in Eq. 3) or V., we can
detennine the hold-up (cid:1) i.e., the film thickness from Eq.(4).
4. EXPERIMENTAL APPARATUS AND PROCEDURE
Two types of the arrangement of the sensor electrodes have been used depending on the
object of the measurement, i.e., to measure the cross-sectionally averaged hold-up or the local values
of the film tckness at each point along, for example, the circumference of channel surface. The
measuring system and procedure of the CECM will be explained below.
4.1 Measurement of the Cross-sectionally Averaged Hold-up, (Type A prove)
In Fig.4 (a) is shown an example of the schematic view of the experimental apparatus of the
CECM for measuring the cross-sectionally averaged hold-up in the case of, for example a circular
pipe with an inner diameter of 19.2 nun. The constant electric current of known value was supplied
from the ring electrodes A and which were ade of brass and embedded flush with the inner
surface of the whole circumference of tube at the axial distance of about 2 m.
The change of voltage drop with time due to the change of hold-up at the objective cross-
section were measured by the sensor electrodes C and D, for example, which were also embedded
flush with the duct surface. The details of the pair of the sensor electrodes is shown in Fig.4 (b).
The distance of one pair of sensor electrodes in the direction of flow can be fundamentally very short,
if necessary I nun for example, which means that the hold-up detected was one averaged over the
volumeincludedinbetweenthesensorelectrodes. twas3O.OnuninthecaseshowninFig.4(b).
This pair of sensor electrodes is referred to as the Type A prove.
The output from each Type A prove, A VCD in Fig.4 (b) for example, was sampled at a
predetermined frequency by an A-D converter, after passing through a high input-impedance aplifier,
and the statistical values, such as time averaged hold-up or the film thickness, the wave height, the
distribution of film thickness and so forth, were calculated from the digitized data.
It must be pointed out that the test section in between the power electrodes must be made of
nonconductive material. Furthermore the leak of the electric current toward the exit of the channel
in Fig.4 (a) for example, must be minimized to keep the electric cuurent constant in the mearsuring
section as well as posible. If the leak can not be stoped, the fluctuation of the electric current is
measured in the section AE in Fig.4 by inserting a resistor with a low electric resistance.
4.2 Measurement of the Local Value of the Film Thickness, (Type prove)
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CONSTANT COMPUTER
CURRENT
SOURCE A/D CONVERT
BOARD
AIR
LIQUID AIR
2830
LIQUID
(a) Schematic view Of h experimental apparatus for the Type A proves of the CECM.
30 mm
0.3mm
7(cid:1)
C
tion Amp.
(b) One pair of electrodes, C and D in Fig.4 (a).
Figs.4 ShematicviewofthesystemoftheTypeAprovesoftheCECM-
B C
Type B probe Plant view
A Water film
Side iew
PU
Po-er so ce
Ifier
romagnetl e
11lograpb er
Fig.5 SchemaficviewofthesystemoftheTypeB(Ringtype) proveoftheCECM.
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In Fig.5 is shown an example of the system for measuring the local value of the time
fluctuating film thickness at a point on the duct surface. In tis case an electrode is consisted of two
concentric rings and one circular rod at the center of the two rings. They are respectively expressed
as A, and C in Fig. 5, and referred to as the Type prove as a whole in the present paper. The
constant current is supplied from the center rod electrode A) and the outermost ring (electrode ,
which are the power electrodes. The signal is detected from h center rod a-rid the rniddle ring
(electrode 13), which are the sensor electrodes. This means that he measured hold-up is averaged
over the sensor electrodes. The diameter of the outermost ring C affects on the uniformity of the
electric current distribution in the region of the sensor electrodes. The larger the better if possible.
The outermost ring is always grounded.
It must be noticed that one constant power source is necessary for one pair of the sensor
electrode in this case. This is one of the defects of the Type prove. The linear relation between
film thickness and output from the sensor electrodes is not so good as the Type A electrode although
possibly better thari conventional one because the electrode C is separated from the sensor electrode ,
then the electric current dnsity distribution is more uniform near the sensor electrodes, i. e., the
center part of the type prove, (electrodes A and B). The dam processing after detecting by the
sensor electrodes is the same as the Type A prove.
Both the Type A and the Type proves have been successfully and properly used in our
experiments depending on the purpose of the experiment
4.3 Constant Current Power Source and Isoladon (High Input Impedance) Amplifier.
The characteristics of a constant electric current power supplier and an isolation amplifier
which we have used are as follows.
(1) Constant Current Power Source;
* Range of the electric current 0 I A - I I mA. The output constant current is
set by the step of O I A by the five digital dials and kept constant even if the electric resistance
between the power electrodes fluctuates in the frequency range less than 10 KHz.
* Range of the output voltage: -2 10 0 Volts.
(2) Isolation Amplifier;
• Input impedance: 2 M fl.
• Frequency range: DC - 3 KHz.
*Output voltage: Maximum ± IO Volts.
* Number of channel: 32
(3) Example of the applied constant electric cur-rent and the range of the voltage difference between the
power electrodes: I mA and about 200 Volts.
The output from the sensor electrode considerably fluctuates depending on the fluctuation
of the local film thickness as will be shown later, but the output voltage of the power electrodes is
small especially in the case of an anular flow or thin film flow with small scale of disturbance waves
because the axial distance between the power electrodes is usualy long and the resistance is averaged
in that section.
5. CALIBRATION
5.1 StaticCalibrationofTypeAprovebyUsingNonconductiveRods[2]-[4]
Static calibration was performed by inserting a cylindrical nonconductive rod with known
diameter into the test section which was initially filled up with water. Te rd had a relatively short
axial length but longer than the axial distance between a pair of the sensor electrodes. The rod was
free from movement in the radial direction but the output from the sensor electrode did not
changed if the rod swung. This fact means that the output was not affected by the radial location
of the nonconductive material, i.e., the types of flow as discussed on the Fig-3.
Figure 6 shows an example of the calibration of the hold-up by using the nonconductive
rods. The horizontal axis is the void ratio which corresponds to the nonconductive rod, and the
vertical axis is the measured void ratio by the CECM. The difference of the symbols means the
difference in the date of the calibration. We made the similar calibration many times and got sirnilar
results. The figure shows that the measured values agree weU with the known void ratio with the
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0.5
o'68.8.9
*'68.8.23
0 0.5 1.0
a
Fig.6 Static calibration by nonconductive rods.
30C
200 -
E
0
0
10C -
o'68.11.26
-'68.12.12
0 100 200 300
Air volume replaced with water cc
Fig-7 Dynamic calibration by a rising large bubble.
1.0
jL -0.1 22 mle
0.8 - it, -0.73 A
jL-O-z- 11 jL -0.1 Mis
0.6 - p,
HUGHMER &P PESSBURG
0.4 SEKOGUCHI
jL-
j. L-2.0ml.
0.2
0,
0.02 3 4 6 8 0.1 2 3 4 6 1.0 2 3 4 6 10
ic / IL
Fig-8 Comparisonofthevoidfrac6onmeasuredbytheTvpeAprobewiththepublisheddata.
229
accuracy of about 3 %, signifying that the data were reproducible as well.
5.2 Dynamic Calibration of Type A Prove by a Rising arge Bubble 21
The time variation of die void fraction was measured by the CECM while a large air bubble
traveled upward through stagnant liquid contained in a vertical circular tube. The volume of the
large bubble was measured in advance and its change with the decrease in the static pressure at the
measuring cross-secLion was corrected. The time trace of the void fraction measured by te
CECM was integrated in order to obtain die total volume of the large bubble passing by the electrode.
The measured values were compared with the known volumes in Fig.7. The difference in te
symbols expresses the difference of the measured date. About 80 of the measured data are within
the accuracy of ± % . This verifies that 'the CECM is useful to measure time fluctuating
instantaneous void fraction even in the case of interri-tittent flows like the slug flow.
5.3 Comparison with the Published Data of Void Fraction in Two-Fhase Flow Condition 2]
The CECM with the Type A prove is considered to be applicable to wider range of flow
patterns because the output is independent of the radial location of gas bubbles as discussed in Figs. I
and 3 The fluctuations of void ratio were measured in the cases of air-water two-phase vertical
upward flows and their time mean values were calculated by using data obtained in the sufficiently
long period. The flow patterns included were the bubbly, die slug and the froth flows. They are
compared with the published data in Fig.8. The vertical axis is the measured hold-up and the
horizontal axis is the ratio of the superficial velocity of air to that of water. It is clear that the hold-up
is a function of the liquid flow rate, i. e., the larger the liquid flow rate, the smaller the hold-up in this
experimental range if compared with the same value of the flow rate ratio of _(cid:1) to j, The trends of
the data points of each researcher are similar and the agreement is quantitatively satisfactory if the
difference of the measuring methods and the wide range of the flow patterns measured are taken
into consideration.
5.4 Cali5ration of the Type prove.
The Type prove has been used only for the measurement in the liquid film flow so far.
The calibration was performed by putting a nonconductive rectangular block with the known gap size
on the Type prove. The linear relation of the output with the gap size was much poorer than the
Type A prove. Then we should have a calibration curve beforhand to determine the hold-up.
6. EXAMPLES OF THE APPLICATION OF THE CECM TO TWO-PHASE FLOW
The CECM has been successfully applied to many cases of two-phase flow especially to the
liquid film. flowing with high speed gas flow. Some of them wiIJ be explained in the following
sections.
6.1 Waves on Liquid Film in a Horizontal Rectangular Duct.
6.1.1 ExperimentalApparatusandObservedFlowPattems[5]
Figure 9 shows a schematic diagram of the experimental apparatus used. The test section
was made of transparent acrylic resin to observe the flow pattern. The height and the width of the
duct were respectively I 0 nun and 40. 0 mm, and the total length was 47 in. Air and water,
which were the working fluids, flew through the film thickness measuring section as a separated flow
or a film flow. Time varying film thickness was simultaneously measured at four axially different
locations by the Type A proves.
Before beginning the measurement of film thickness the calibration of the output from the
proves was perfortned. by using several nonconductive rectangular rods each of which formed a gap
with known size between the rod and the bottom of the rectangular duct where the proves were
mounted flush with the bottom.
In Fig. 0 is shown the flow conditions of the experiment by the marks and 0. The
vertical axis r is the water volumetric flow rate per unit width and the horizontal axis, G1 is the air
superficial velocity. In the figure the boundary of the flow patterns observed are also shown, A
being for the annular flow, D for the disturbance wave flow, P for the pebble wave flow, R for the
ripple flow, for the smooth surface flow, T for the two-dimensional wave flow and V for the
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( Ar flter T:Theremometer M
Reducing alve m m :U-tube manc-
Orifice flo(cid:1) meter 3 mater
(pConstant head tk V :alves
(3)Rotame ter 1
Alr-ater mixing
section
PUMP
(J)W:r:r.,,totage tank (D(LTV, C3
(2) p r tor
Measurin5 section
PmOlLin thickness
3500
4100
(1)
T V4
Fig.9 Flow system of a horizontal rectangular duct.
3
2
A
0
I-
lo- 4 0 0 0 0
E a6 0 P 0 0 0 0
R
E 4 - 0 0 0 00 0 00 00 00 000
3- 0 0 0 00
S 00
2- 0 N 0 000
0
lo-, 0 0 0 I.L f I IL LLU
60 80
2 3 4 6 8 10 20 0 40
jG M/S
Fig. 10 Flow patterns observed and the experimental conditions.
-44-10snAsm I- to S =!d
S
jG 5 MIS r, &0-10,5 Sm p, to S
T
e Hip NOWN, R
6 ml s r ts jcr4 ml sm p*___ Lo s
P
ic;'30mis r.6D.10 Sm to S
R
jr= SIS r-10-10-4 SM I- Inc
D
W-
JG'40Mts F-4.0-10'4 SM IDS
A
Fig. I I Traces of film thickness of the typical flow patterns.
231
viscous wave flow. NW stands for the non-wetting flow in wich the break of die liquid film
occurred at some parts on the bottom surface of the duct.
Distinct feature of waves appearing on the gas-liquid interfacein die respective flow regime
can be recognized by die time traces of the fm thickness measured by die CECM. Typical
examples are show i Fig. I I with the notation of te flow pattern on the right side of the figure.
6.1.2 Frequency Distributions of die Film Thickness, (cid:1).[5]-[8]
The cumulative frequency distributions, which are equivalent to the probability functions,
are plotted on a normal probability paper, as shown in Fig. 2 for the respective typical flow patter R,
T, P and D. If the line is straight, the probability of the fm thickness is expressed by a normal
distribution. It is clearly seen that the distribution of the film thickness is expressed by a sraight line
in the case of the pebble wave flow, signifying that the fm thickness distribution is approximately
normal in this flow pattern. On the other hand in the case of the disturbance wave flow the data
points can be approximated by two segments with the larger and the smaller parts of t which
respectively correspond to the disturbance waves and the base waves.
In Fig. 13 are shown the changes of the cumulative frequency distribution curves with the
changes of the flow conditions across the transition region of the flow pattern from the pebble wave
region to the disturbance wave region. Ibis figure shows that by increasing only a small amount
of liquid flow rate causes a drastic change of the flow pattern from the pebble wave to the disturbance
wave flow. Then the wave height increases abruptly at the boundary. On the other hand the
transition region between the disturbance wave flow and the ripple flow is wide and the distribution
gradually changes with increasing in the both air and water flow rates as shown in Fig. 14.
6.1.3 Generation of Viscous Wave 9]
Figure 15 shows the typical examples of the time variation of film thickness which were
measured by the type prove at the center of the duct width of the rectangular test section 40 mm
width and 10 mm height) They were obtained under the different water flow rate conditions with
the air flow rate kept constant as shown by solid circles in Fig. 0. Capital letters written on the right
side of Fig. express the flow pattems.
Comparison of the flow rates in Figs. 10 and 15 reveals that by decreasing a smal aount
of water flow rate an interesting wave generates on the surface of thin film in the region below the
smooth surface flow region (S-region) as expressed by the V-region in Fig. 0. As clearly seen in
Fig. 5 the wave number is much smaller than those of the P - and the T - waves. Ibis interesting
wave is referred to as the viscous wave in our papers. The definition of the viscous wave is that its
wave velocity is less than the fluid particle velocity at the interface of the liquid film.
The generation of the viscous wave was theoretically discussed based on the Or-
Sommerfeld equation. The controlling parameter of the generation of the viscous wave is the
film thickness. The theoretically obtained film thickness of the generation of the viscous wave is
(4) =0.255 mm as shown by the thick dotted line in Fig. 16. On the other hand the boundary of the
generation of the viscous wave, which was obtained experimentally as the boundary between the
marks and in Fig. 16, is expressed by the thick solid fine. This line is on the contour line of
the film thickness of (4).40.26 mrrL The agreement of those two fines expressing the onset of
the viscous wave is quite satisfactory.
6.2 Flow in a Horizontal Capillary Tube 10]
The time varying void fluctuations were rneasured by the Type A proves in the case of air-
water two-phase mixture flowing in a horizontal capillary tube with the inner diameter, D, of 10 24
and 49 mm.
6.2.1 Calibration of the Type A prove.
Figure 17 shows the calibration of the Type A prove of the CECM for annular type of flow
by inserting a long nonconductive rod in some cases or several long rods with the smaller diameters
in the other cases. The vertical axis is te reciprocal of the hold-up, I/ and the horizontal axis is
the same quantity but obtained by the nonconductive rods. The agreement of the theoretical values
(horizontal axis) and the measured values (vertical axis) is quite satisfactory even when the plural
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