- Email: [email protected]
Improving the accuracy of the capacitance method for void fraction measurement
ELSEVIER
Improving the Accuracy of the Capacitance Method for Void Fraction Measurement Abdullah A. Kendoush Zareh A. Sarkis Iraqi Atomic Energy Commission, Baghdad, Iraq
• Void fraction measurements were made using capacitance method. Five capacitor configurations were manufactured and tested; parallel, strip-type plates, ring-type plates, unidirectional, and double-helix. The void fraction was simulated by nonflow air-paraffin wax, air-glass, air-wood, and air-Freon 113 systems. The relative statistical error in void fraction measurement was minimized by taking into account the spacing between the ends of the two electrodes.
Keywords: two-phase flow, void fraction, annular flow, core flow, capacitance method INTRODUCTION The void fraction of two-phase, gas-liquid flow is defined as the ratio of the volume of gas to the total volume of gas-liquid mixture in a finite length of the pipeline. The void fraction is an important quantity in measuring and predicting the average density, pressure drop, flow pattern, etc. of a flowing gas-liquid mixture in a pipe. Nuclear radiation attenuation methods have been used for the measurement of void fraction [1] and are considered nonintrusive as they do not cause perturbation of the local two-phase flow. In situations where these methods cannot be used, one can rely on the use of another nonintrusive device, the capacitor. The capacitance method makes use of the differences between the dielectric properties of gases and liquids. Capacitance methods have been used for the measurement of void fraction by inserting the devices in the flow in fluidized beds. Intrusive methods used for void fraction measurements include hot-wire and hot-film anemometry, fiber-optic probes, microthermocouples, isokinetic sampling, and electrical conductivity probes. Duckier and Bergelin [2] and Taibly and Portalski [3] used the capacitance method to measure the film thickness and wave profile of falling liquid films. Abouelwafa and Kendall [4] examined six capacitor configurations for determining the void fraction. They concluded that the most practical linear capacitor was the double helix if used at a frequency of 1 MHz. Chun and Sung [5] derived a set of theoretical equations for the "use of capacitors in void fraction measurements. They assumed that there was no spacing between the ends of the two electrodes, and this assumption produced an error in their void fraction results. In our work this source of error was eliminated and an experimental program was conducted to determine the effects of the following pa-
rameters on measuring void fraction by the capacitance method: 1. 2. 3. 4.
Material and thickness of tube wall of test section Geometry, size, and material of electrodes Simulated two-phase flow regimes Measuring instruments THEORY
The following theoretical derivations are analogous to those considered by Chun and Sung [5] except for the inclusion of the electrode spacing z, which they neglected. The relative capacitance C* for core and annular flows was analyzed by means of a simplified geometrical mapping and the concept of adding capacitances in series and parallel. Figure l a represents a cross section of a test section with a pair of strip-type electrodes for the measurement of void fraction in an annular or core two-phase flow simulation. The void fraction a is given as
a = ( d / D ) 2.
(1)
Figure l b is an equivalent cross section of the same test section obtained by graphical mapping using flux lines and equipotentials. The following geometrical relationships were used to relate the two figures: 1rD a z; b = D; 2 h
~-d 2
~-D 2
d=e=Dv~-;
(2)
f = (b - e ) / 2 = O(1 - vra-~)/2;
g = (a - h ) / 2 = ( z r D / 4 ) ( 1 - v~-) - ( z / 2 ) . If the permittivities of the coaxial dielectric cylinders of
Address correspondence to Dr. Abdullah Abbas Kendoush, P.O. Box 28432, 12631 Baghdad, Iraq.
Experimental Thermal and Fluid Science 1995; 11:321-326 © Elsevier Science Inc., 1995 655 Avenue of the Americas, New York, NY 10010
0894-1777/95/$9.50 SSDI 0894-1777(95)00035-K
322
A . A . Kendoush and Z. A. 8arkis a
Table 1. Experimental Test Sections
Item
l a
2
b
3 4
Test-Section Material
O.D. (cm)
LD. (cm)
Length (cm)
Sensitit,ity" ( 6 C / &x ) (pF)
Stainless steel Galvanized steel Perspex Glass
4.84
4.1
50
1 X 10 3
4.9
3.9
50
1 × 10 3
5.0 5.5 5.5 4.5 4.0 3.0
3.8 4.9 4.4 4.0 3.6 2.6
50 50 50 40 40 40
40 65 65 65 65 65
The sensitivity measured for strip-type capacitor. e
for core flow and e 1 > e 2, and
Figure 1. Cross section of a strip-type capacitor (a) and an equivalent cross section (b), and (c).
ae2(1 -- 2 z / r r D ) C* = 1 -
(10) (E 1 - E:)(fc~ - a ) + E2(1 - 2 z / T r D )
Fig. l a are e~ and E2, t h e n the total c a p a c i t a n c e C of the system is
C=
'
+
+--
C21 "~ C22 -[- C23
L~re2(l
-
2z/~D)[e2(1
')
EXPERIMENTAL
C3 -
Test ~
2z/~D) +
-
el~/~-a ]
2 [ ( e , - E2)(v~-a - c~) + e2(1 - 2 z / T r O ) ] (3) w h e r e L is the axial length of the e l e c t r o d e , aL C 1 = C3 ~ E 2 f
for a n n u l a r flow and e, > e 2. E q u a t i o n s (3), (5), (6), (9), and (10) r e d u c e to the e q u a t i o n s d e r i v e d by C h u n and Sung [5] w h e n z = 0.
gL C21 = C23
E2--~ e
hL C22
el
e
(4) W h e n cr = 0 (i.e., tube filled with liquid or solid), we get f r o m Eq. (3) C = C o = LTre2(1 - 2 z / T r D ) / 2 ,
(5)
and w h e n a = 1 (i.e., e m p t y t u b e ) we get C = C l = LTr(e I - 2e2z/~rD)/2.
(6)
By eliminating the effects of cables and the test section on m e a s u r e d v o i d fraction, the relative c a p a c i t a n c e C* is defined as C * = ( C - C o ) / ( C 1 - C O)
when e I > e2
(7)
C * = ( C - C o ) / ( C o - C 1)
w h e n e I < E2.
(8)
APPARATUS
Sections
A nonflow system of m e a s u r e m e n t was used with tubular test sections of stainless steel, galvanized steel, pe spex, and glass. It was f o u n d that perspex and glass g~v~ _ :tter sensitivity for void fraction m e a s u r e m e n t than the steels• T h e r e f o r e , it was d e c i d e d to vary the thickness of the perspex and glass tubes, which did not affect the sensitivity of the m e a s u r e d void fraction. T a b l e 1 gives the details of the test section. T h e sensitivity ( 6 C / 6 c e ) is defined as the difference in the m e a n values of the capacitances for filled ( a = 0) and e m p t y ( a = 1) test sections. Flow
Simulations
F l o w patterns w e r e simulated in static conditions by a p r o p e r c o m b i n a t i o n of two materials having different dielectric coefficients e R, defined as e n = E / e 0, w h e r e e 0 is the permittivity of the vacuum. A c t u a l values of void fraction w e r e calculated by inserting k n o w n g e o m e t r i c a l sizes of simulation materials into the test section, with an accuracy of + 1 × 10 3. T h e materials used in flow simulations are listed in T a b l e 2. F o r the case of air F r e o n 113 a special system was designed in which the airflow was allowed to pass through a T a b l e 2. Experimental Flow Simulation Materials
and
Substituting Eqs. (3), (5), and (6) into (7) and (8), the following e q u a t i o n s w e r e o b t a i n e d , tee2(1 -- 2 z / T r D ) C* =
(9) ( e I - e2)(~-ce - c~) + e2(1 - 2 z / T r D )
Item
Material
1
Air
2 3 4 5
Glass Paraffin wax Wood Freon 113
a From Refs. 5 and 6.
Flow Simulation
Dielectric ConstanU en
--
1.0
Core Core, annular Core, annular Annular, bubbly
3.8 2.25 2.6 2.5
Improving the Accuracy of Capacitance Method
323
column of liquid Freon 113. The actual void fraction was measured by both the neutron transmission technique and the difference in the liquid level of the column. Instrumentation
Five capacitor configurations were examined as shown in Figure 2. They were parallel plates, strip-type plates, ringtype plates, unidirectional capacitor, and double-helix capacitor. These capacitors were placed on the outer surface of the test section. They were constructed from aluminum and copper plates of different thicknesses. However, the capacitor materials and thicknesses used here did not have any noticeable effect on the sensitivity of the void fraction measurements. Strip-type capacitors were chosen to study the effects of capacitor length-to-diameter ratio on the void fraction sensitivity and accuracy. The capacitance was measured by two methods, (1) with an LRC meter and (2) with an integrated circuit. The LRC meter (General Radio, USA) was of 1 kHz frequency and 2 V bias, with + 4% accuracy in the picofarad range. The integrated circuit was designed and built in the laboratory. The results of this circuit were in agreement with those obtained with the LRC meter. The overall accuracy of measurement was + 1 pF in the capacitance range > 100 p F a n d +0.01 p F i n the range < 100 pF for all types of capacitors and throughout the void fraction range. RESULTS AND DISCUSSION Experimental runs were carried out using all the types of capacitors shown in Fig. 2. Each capacitor configuration was tested with all the types of test sections listed in Table 1 and with all the flow simulation materials of Table 2. The aim was to examine, calibrate, and compare these kinds of capacitors as void sensors. The nonelectrolytic nature of the materials of Table 2 was the prime reason for their use. Electrolytic materials (e.g., water) need high frequencies ( > 1 kHz) for the measurement of void fraction by the capacitance method. Figures 3-7 show calibration test runs for the ring, unidirectional, double-helix, parallel-plate and strip-type capacitors, respectively. Table 3 shows a comparison of the five types of capacitors. The low sensitivities exhibited by the double-helix and unidirectional capacitors made them unsuitable for accurate void fraction measurements with the flow pattern and flow simulation materials of Table 3. In view of the higher sensitivities of the strip and parallel-plate capacitors, it was plausible to concentrate subsequent experimental effort on their analysis, comparison, and optimization, as is shown in the following results. However, the behavior of the ring-type capacitor was somewhere between the two extremes. Simulated flow void fractions were measured using strip-type capacitors 2.5, 5, 7.5, and 10 cm in length placed on the outer surface of a 5-cm O.D. test section. Figure 8 represents least-square fitted curves for the various L/D ratios and shows that the best accuracy is obtained when L/D > 1. Note that the percent relative error in Fig. 8 represents 6a/o~ (i.e., the uncertainty in the void fraction measurement). Figure 9 shows a comparison between Eqs. (9) and (10) and their equivalent in Chun and Sung's paper [5] allowing for an electrode spacing of z = 0.7 cm between the
b
dO--
Figure 2, The experimental capacitor configurations (a) Parallel plates; (b) strip-type plates; (c) ring-type plates; (d) unidirectional; (e) double-helix.
ends of the electrodes of the strip-type capacitor and for
L/D = 2. Note the increase in the accuracy obtained in the void fraction as a result of the inclusion of the electrode spacing in the present analysis. Equations (9) and (10) can be used for the parallel-plate capacitor by substituting D for z. The theoretical results led to the design of a parallel-plate capacitor placed on the outer surface of a perspex test section of 5-cm O.D. and with L/D = 2. Using this type of void sensor, the void fraction measurements were carried out, with the results shown in Fig. 10, which shows a comparison between the equations of Chun and Sung [5] and the present Eqs. (9) and (10). The accuracy of Eqs. (9) and (10) in predicting the void fraction is superior to that of Chun
324
A . A . Kendoush and Z. A. Sarkis 6.5J
532k
.
.
.
.
.
.
.
.
PERSPEX TEST SECTION
J\
t6.01
15.0
s12 14.0
5O8
0.0
0'1
0'2
~
d.~
~s
~.6
0'.7
d.8
69
10
ACTUAL VOID FRACTION
Figure 3. Calibration curve of the ring-type capacitor with air-paraffin wax and core flow simulation.
and Sung [5], who neglected the electrode spacing. It should be noted that shielding and grounding of these capacitors give additional accuracy to the void fraction measurements as shown in Fig. 10.
CONCLUSIONS 1. The main difference between the present and reported [5] analyses was the inclusion of the electrode spacing (z) between the ends of the two capacitor plates which minimized the relative statistical error in the void fraction results. 2. The best accuracy in void fraction measurements was obtained when the ratio of capacitor length to test-section diameter was greater than unity. 3. Nonelectrolytic liquids such as Freon 113 were suitable for measurements of void fraction by the capacitance technique, whereas electrolytic liquids such as water need high frequencies ( > 1 kHz) for such measurements.
13.0
0.0
04
0.2
03 0.4. 04 ACTUAL V0]D
0,8
0.9
~s,o
Figure 5. Calibration curves of the double-helix capacitor. Top curve ( • ) annular flow, air-wood. Other curves, from the bottom: core flow ( I ) air glass, ( 0 ) air-paraffin wax, (-k) air-wood. PRACTICAL USEFULNESS AND FUTURE RESEARCH The main advantages of the capacitance method for void fraction measurement in two-phase one- or two-component flow are its ruggedness, versatility, and nonintrusion with the flow medium. The following are suggested subjects for future work: 1. A comparative study of the capacitance method and the radiation attenuation technique [1] for void fraction measurement in both transient and steady-state twophase flow systems. 2. Flow pattern prediction with the capacitance method,
3.2
' ' ' ' PERSPEX
bd U Z
o.s 0.7 FRACTION
TEST SECTION o.
390
ao
Z
~2.g
380
~ 2.a
"-;:'AIR_PARAFFINV
ne
~
A
~
•< 3?0
~ 2.7
36(
2.%
o.'1
42
63
,~.4 6s 60 67 ACTUAL~OID FRACTION
68 ob 1.o
Figure 4. Calibration curves for unidirectional capacitor with core flow field,
I
0.0
02
,
i
0./,
,
I
0.6
,
I
0.B
1.0
ACTUAL VOID FRACTION Figure 6. Calibration curve of the parallel-plate capacitor with air-paraffin wax and core flow simulation.
Improving the Accuracy of Capacitance Method
325
Table 3. A Comparison of the Five Capacitor Types
Average Capacitance C 1 (ce = 1) CO (a = (pF) (pF)
Test-Section Material
Capacitor T y p e Parallel plates Strip
Perspex Glass
368.5 598 598 675 601 509 2.76 2.76 12.5 12.5 12.85
Perspex Ring Unidirectional
Perspex Perspex
Double helix
Perspex
Sensitivity ( 6C / 6a ) (pF)
O)
399.5 665 662 700 678 533 3.12 2.87 16.5 14.2 16.4
Flow-Simulation Materials
31.0 72.0 60.0 25.0 77.0 24.0 0.36 0.11 4.0 1.7 3.55
with the time trace recorded in two-phase flow pipe2a~ lines. 3. The effects of using other materials of capacitors on 24.0 void fraction m e a s u r e m e n t - - f o r example, tantalum foils, polyester dielectrics, polystyrene foils, silvered r i o 20.0 mica, and metallized paper. 4. The influence of irregularities in the actual two-phase p-, flow patterns on the accuracy of void fraction measure- l a d 16.0 ment by capacitors. 12.0
L,d=as
Air-paraffin Air-wood Air-paraffin Air-Glass Air-wood Air-paraffin Air-wood Air-paraffin Air-wood Air-paraffin Air-wood
.
1~=1.0
.
.
.
Flow Pattern
wax
Core Core Core Core Annular Core Core Core Core Core Annular
wax
wax wax wax
.
.
.
.
.~,2
W OC
NOMENCLATURE
a,b,d-h C C* Co
-- 7
0
constants defined by Eq. (2), m total capacitance, F relative capacitance, dimensionless capacitance at a = 0, F
0
I
I
~
I
~.0
=" 0)
0~
0'2
[
d~ d~ d~ 0 ACTUAL VOID F R A C T I O N
0.'3
~
.
d.9
1.0
Figure 8. Experimental optimization of the L / D ratio for the strip-type capacitor.
14 u_ ta
L i I i
12
'-~ 65C tJ
i
Z
10
~J
\
1 \
0
\
h*
\
~
575
0.0
,
n
n
m
0.2
0./*
0.6
0.8
1.0
ACTUAL VOID FRACTION
Figure 7. Calibration curves of the strip-type capacitor. Perspex test section: air-glass, core flow (0). Glass test section: core flow (m) air-paraffin wax, (©) air-wood, core flow (*) air-wood annular flow.
,v/
,~---E.~perimentot results using
Chun ¢ Sung IS:]equatFons(crosses)
k
k
60o
\
\~
x
/
~Experimentol results usinQ present equations(g)&(10}
(circles)
0 O.0
0.1
0.2
03 0.4 0.5 0.6 0.7 ACTUAL VOID FRACTION
0.8
0.9
1.0
Figure 9. Experimental validation of the theoretical results for the strip-type capacitor and air-paraffin wax core flow simulation.
326
A . A . Kendoush and Z. A. Sarkis
70
60
~
~,, A~ \
50
A : CHUN& SUNG(53 EQUATIONS B : PRESENT EQUATIONS(g)&(t0} C : SHIELDED CAPACITOR
nr
L~ I.a.I
4O
z
spacing b e t w e e n the ends of the two electrodes, m
O/
void fraction, dimensionless permittivities of fluids 1 and 2, C 2 / ( N m-) dielectric constant, dimensionless
Greek Symbols E 1, E 2
eR
30
REFERENCES
ILl n,"
.-e 20 10 00
i
0.0
0'.1
0.2
i
|
?o
0.3 0.4 0.5 0.6 0.7 ACTUAL VOID FRACTION
v
0.8
i
0.9
Figure 10. Experimental results of the parallel-plate capacitor and air-paraffin wax core flow simulation.
CI Cl, C21, C22, C23, C 3
D d L
c a p a c i t a n c e at a = 1, F constants defined by Eq. (4), C 2 / ( N m) o u t e r d i a m e t e r o f test section, m o u t e r d i a m e t e r of fluid I in the test section, m axial e l e c t r o d e length, m
1.0
1. Kendoush, A. A., A Comparative Study of the Various Nuclear Radiations Used for Void Fraction Measurements, Nucl. Eng. Des. 137, 249-257, 1992. 2. Duckier, A. E., and Bergelin, O. P., Characteristics of Flow in Falling Liquid Films, Chem. Eng. Prog. 48, 557-563, 1952. 3. Tailby, S. R., and Portalski, S., The Hydrodynamics of Liquid Films Flow on a Vertical Surface, Trans. Inst. Chem. Eng., 38, 324-330, 1960. 4. Abouelwafa, S., and Kendall, J. M., The Use of Capacitance Sensors for Phase Percentage Determination in Multiphase Pipelines, IEEE Trans. Instrum. Measure, IM-29, 24-29, 1980. 5. Chun, M.-H., and Sung, C.-K., Parametric Effects on the Void Fraction Measurement by Capacitance Transducers, Int. J. Multiphase Flow 12, 627 640, 1986. 6. Fink, D. G., and Carroll, J. M., Standard Handbook for Electrical Engineers, McGraw-Hill, New York, 1968.
Received September 6, 1994; revised March 6, 1995
Improving the Accuracy of the Capacitance Method for Void Fraction Measurement Abdullah A. Kendoush Zareh A. Sarkis Iraqi Atomic Energy Commission, Baghdad, Iraq
• Void fraction measurements were made using capacitance method. Five capacitor configurations were manufactured and tested; parallel, strip-type plates, ring-type plates, unidirectional, and double-helix. The void fraction was simulated by nonflow air-paraffin wax, air-glass, air-wood, and air-Freon 113 systems. The relative statistical error in void fraction measurement was minimized by taking into account the spacing between the ends of the two electrodes.
Keywords: two-phase flow, void fraction, annular flow, core flow, capacitance method INTRODUCTION The void fraction of two-phase, gas-liquid flow is defined as the ratio of the volume of gas to the total volume of gas-liquid mixture in a finite length of the pipeline. The void fraction is an important quantity in measuring and predicting the average density, pressure drop, flow pattern, etc. of a flowing gas-liquid mixture in a pipe. Nuclear radiation attenuation methods have been used for the measurement of void fraction [1] and are considered nonintrusive as they do not cause perturbation of the local two-phase flow. In situations where these methods cannot be used, one can rely on the use of another nonintrusive device, the capacitor. The capacitance method makes use of the differences between the dielectric properties of gases and liquids. Capacitance methods have been used for the measurement of void fraction by inserting the devices in the flow in fluidized beds. Intrusive methods used for void fraction measurements include hot-wire and hot-film anemometry, fiber-optic probes, microthermocouples, isokinetic sampling, and electrical conductivity probes. Duckier and Bergelin [2] and Taibly and Portalski [3] used the capacitance method to measure the film thickness and wave profile of falling liquid films. Abouelwafa and Kendall [4] examined six capacitor configurations for determining the void fraction. They concluded that the most practical linear capacitor was the double helix if used at a frequency of 1 MHz. Chun and Sung [5] derived a set of theoretical equations for the "use of capacitors in void fraction measurements. They assumed that there was no spacing between the ends of the two electrodes, and this assumption produced an error in their void fraction results. In our work this source of error was eliminated and an experimental program was conducted to determine the effects of the following pa-
rameters on measuring void fraction by the capacitance method: 1. 2. 3. 4.
Material and thickness of tube wall of test section Geometry, size, and material of electrodes Simulated two-phase flow regimes Measuring instruments THEORY
The following theoretical derivations are analogous to those considered by Chun and Sung [5] except for the inclusion of the electrode spacing z, which they neglected. The relative capacitance C* for core and annular flows was analyzed by means of a simplified geometrical mapping and the concept of adding capacitances in series and parallel. Figure l a represents a cross section of a test section with a pair of strip-type electrodes for the measurement of void fraction in an annular or core two-phase flow simulation. The void fraction a is given as
a = ( d / D ) 2.
(1)
Figure l b is an equivalent cross section of the same test section obtained by graphical mapping using flux lines and equipotentials. The following geometrical relationships were used to relate the two figures: 1rD a z; b = D; 2 h
~-d 2
~-D 2
d=e=Dv~-;
(2)
f = (b - e ) / 2 = O(1 - vra-~)/2;
g = (a - h ) / 2 = ( z r D / 4 ) ( 1 - v~-) - ( z / 2 ) . If the permittivities of the coaxial dielectric cylinders of
Address correspondence to Dr. Abdullah Abbas Kendoush, P.O. Box 28432, 12631 Baghdad, Iraq.
Experimental Thermal and Fluid Science 1995; 11:321-326 © Elsevier Science Inc., 1995 655 Avenue of the Americas, New York, NY 10010
0894-1777/95/$9.50 SSDI 0894-1777(95)00035-K
322
A . A . Kendoush and Z. A. 8arkis a
Table 1. Experimental Test Sections
Item
l a
2
b
3 4
Test-Section Material
O.D. (cm)
LD. (cm)
Length (cm)
Sensitit,ity" ( 6 C / &x ) (pF)
Stainless steel Galvanized steel Perspex Glass
4.84
4.1
50
1 X 10 3
4.9
3.9
50
1 × 10 3
5.0 5.5 5.5 4.5 4.0 3.0
3.8 4.9 4.4 4.0 3.6 2.6
50 50 50 40 40 40
40 65 65 65 65 65
The sensitivity measured for strip-type capacitor. e
for core flow and e 1 > e 2, and
Figure 1. Cross section of a strip-type capacitor (a) and an equivalent cross section (b), and (c).
ae2(1 -- 2 z / r r D ) C* = 1 -
(10) (E 1 - E:)(fc~ - a ) + E2(1 - 2 z / T r D )
Fig. l a are e~ and E2, t h e n the total c a p a c i t a n c e C of the system is
C=
'
+
+--
C21 "~ C22 -[- C23
L~re2(l
-
2z/~D)[e2(1
')
EXPERIMENTAL
C3 -
Test ~
2z/~D) +
-
el~/~-a ]
2 [ ( e , - E2)(v~-a - c~) + e2(1 - 2 z / T r O ) ] (3) w h e r e L is the axial length of the e l e c t r o d e , aL C 1 = C3 ~ E 2 f
for a n n u l a r flow and e, > e 2. E q u a t i o n s (3), (5), (6), (9), and (10) r e d u c e to the e q u a t i o n s d e r i v e d by C h u n and Sung [5] w h e n z = 0.
gL C21 = C23
E2--~ e
hL C22
el
e
(4) W h e n cr = 0 (i.e., tube filled with liquid or solid), we get f r o m Eq. (3) C = C o = LTre2(1 - 2 z / T r D ) / 2 ,
(5)
and w h e n a = 1 (i.e., e m p t y t u b e ) we get C = C l = LTr(e I - 2e2z/~rD)/2.
(6)
By eliminating the effects of cables and the test section on m e a s u r e d v o i d fraction, the relative c a p a c i t a n c e C* is defined as C * = ( C - C o ) / ( C 1 - C O)
when e I > e2
(7)
C * = ( C - C o ) / ( C o - C 1)
w h e n e I < E2.
(8)
APPARATUS
Sections
A nonflow system of m e a s u r e m e n t was used with tubular test sections of stainless steel, galvanized steel, pe spex, and glass. It was f o u n d that perspex and glass g~v~ _ :tter sensitivity for void fraction m e a s u r e m e n t than the steels• T h e r e f o r e , it was d e c i d e d to vary the thickness of the perspex and glass tubes, which did not affect the sensitivity of the m e a s u r e d void fraction. T a b l e 1 gives the details of the test section. T h e sensitivity ( 6 C / 6 c e ) is defined as the difference in the m e a n values of the capacitances for filled ( a = 0) and e m p t y ( a = 1) test sections. Flow
Simulations
F l o w patterns w e r e simulated in static conditions by a p r o p e r c o m b i n a t i o n of two materials having different dielectric coefficients e R, defined as e n = E / e 0, w h e r e e 0 is the permittivity of the vacuum. A c t u a l values of void fraction w e r e calculated by inserting k n o w n g e o m e t r i c a l sizes of simulation materials into the test section, with an accuracy of + 1 × 10 3. T h e materials used in flow simulations are listed in T a b l e 2. F o r the case of air F r e o n 113 a special system was designed in which the airflow was allowed to pass through a T a b l e 2. Experimental Flow Simulation Materials
and
Substituting Eqs. (3), (5), and (6) into (7) and (8), the following e q u a t i o n s w e r e o b t a i n e d , tee2(1 -- 2 z / T r D ) C* =
(9) ( e I - e2)(~-ce - c~) + e2(1 - 2 z / T r D )
Item
Material
1
Air
2 3 4 5
Glass Paraffin wax Wood Freon 113
a From Refs. 5 and 6.
Flow Simulation
Dielectric ConstanU en
--
1.0
Core Core, annular Core, annular Annular, bubbly
3.8 2.25 2.6 2.5
Improving the Accuracy of Capacitance Method
323
column of liquid Freon 113. The actual void fraction was measured by both the neutron transmission technique and the difference in the liquid level of the column. Instrumentation
Five capacitor configurations were examined as shown in Figure 2. They were parallel plates, strip-type plates, ringtype plates, unidirectional capacitor, and double-helix capacitor. These capacitors were placed on the outer surface of the test section. They were constructed from aluminum and copper plates of different thicknesses. However, the capacitor materials and thicknesses used here did not have any noticeable effect on the sensitivity of the void fraction measurements. Strip-type capacitors were chosen to study the effects of capacitor length-to-diameter ratio on the void fraction sensitivity and accuracy. The capacitance was measured by two methods, (1) with an LRC meter and (2) with an integrated circuit. The LRC meter (General Radio, USA) was of 1 kHz frequency and 2 V bias, with + 4% accuracy in the picofarad range. The integrated circuit was designed and built in the laboratory. The results of this circuit were in agreement with those obtained with the LRC meter. The overall accuracy of measurement was + 1 pF in the capacitance range > 100 p F a n d +0.01 p F i n the range < 100 pF for all types of capacitors and throughout the void fraction range. RESULTS AND DISCUSSION Experimental runs were carried out using all the types of capacitors shown in Fig. 2. Each capacitor configuration was tested with all the types of test sections listed in Table 1 and with all the flow simulation materials of Table 2. The aim was to examine, calibrate, and compare these kinds of capacitors as void sensors. The nonelectrolytic nature of the materials of Table 2 was the prime reason for their use. Electrolytic materials (e.g., water) need high frequencies ( > 1 kHz) for the measurement of void fraction by the capacitance method. Figures 3-7 show calibration test runs for the ring, unidirectional, double-helix, parallel-plate and strip-type capacitors, respectively. Table 3 shows a comparison of the five types of capacitors. The low sensitivities exhibited by the double-helix and unidirectional capacitors made them unsuitable for accurate void fraction measurements with the flow pattern and flow simulation materials of Table 3. In view of the higher sensitivities of the strip and parallel-plate capacitors, it was plausible to concentrate subsequent experimental effort on their analysis, comparison, and optimization, as is shown in the following results. However, the behavior of the ring-type capacitor was somewhere between the two extremes. Simulated flow void fractions were measured using strip-type capacitors 2.5, 5, 7.5, and 10 cm in length placed on the outer surface of a 5-cm O.D. test section. Figure 8 represents least-square fitted curves for the various L/D ratios and shows that the best accuracy is obtained when L/D > 1. Note that the percent relative error in Fig. 8 represents 6a/o~ (i.e., the uncertainty in the void fraction measurement). Figure 9 shows a comparison between Eqs. (9) and (10) and their equivalent in Chun and Sung's paper [5] allowing for an electrode spacing of z = 0.7 cm between the
b
dO--
Figure 2, The experimental capacitor configurations (a) Parallel plates; (b) strip-type plates; (c) ring-type plates; (d) unidirectional; (e) double-helix.
ends of the electrodes of the strip-type capacitor and for
L/D = 2. Note the increase in the accuracy obtained in the void fraction as a result of the inclusion of the electrode spacing in the present analysis. Equations (9) and (10) can be used for the parallel-plate capacitor by substituting D for z. The theoretical results led to the design of a parallel-plate capacitor placed on the outer surface of a perspex test section of 5-cm O.D. and with L/D = 2. Using this type of void sensor, the void fraction measurements were carried out, with the results shown in Fig. 10, which shows a comparison between the equations of Chun and Sung [5] and the present Eqs. (9) and (10). The accuracy of Eqs. (9) and (10) in predicting the void fraction is superior to that of Chun
324
A . A . Kendoush and Z. A. Sarkis 6.5J
532k
.
.
.
.
.
.
.
.
PERSPEX TEST SECTION
J\
t6.01
15.0
s12 14.0
5O8
0.0
0'1
0'2
~
d.~
~s
~.6
0'.7
d.8
69
10
ACTUAL VOID FRACTION
Figure 3. Calibration curve of the ring-type capacitor with air-paraffin wax and core flow simulation.
and Sung [5], who neglected the electrode spacing. It should be noted that shielding and grounding of these capacitors give additional accuracy to the void fraction measurements as shown in Fig. 10.
CONCLUSIONS 1. The main difference between the present and reported [5] analyses was the inclusion of the electrode spacing (z) between the ends of the two capacitor plates which minimized the relative statistical error in the void fraction results. 2. The best accuracy in void fraction measurements was obtained when the ratio of capacitor length to test-section diameter was greater than unity. 3. Nonelectrolytic liquids such as Freon 113 were suitable for measurements of void fraction by the capacitance technique, whereas electrolytic liquids such as water need high frequencies ( > 1 kHz) for such measurements.
13.0
0.0
04
0.2
03 0.4. 04 ACTUAL V0]D
0,8
0.9
~s,o
Figure 5. Calibration curves of the double-helix capacitor. Top curve ( • ) annular flow, air-wood. Other curves, from the bottom: core flow ( I ) air glass, ( 0 ) air-paraffin wax, (-k) air-wood. PRACTICAL USEFULNESS AND FUTURE RESEARCH The main advantages of the capacitance method for void fraction measurement in two-phase one- or two-component flow are its ruggedness, versatility, and nonintrusion with the flow medium. The following are suggested subjects for future work: 1. A comparative study of the capacitance method and the radiation attenuation technique [1] for void fraction measurement in both transient and steady-state twophase flow systems. 2. Flow pattern prediction with the capacitance method,
3.2
' ' ' ' PERSPEX
bd U Z
o.s 0.7 FRACTION
TEST SECTION o.
390
ao
Z
~2.g
380
~ 2.a
"-;:'AIR_PARAFFINV
ne
~
A
~
•< 3?0
~ 2.7
36(
2.%
o.'1
42
63
,~.4 6s 60 67 ACTUAL~OID FRACTION
68 ob 1.o
Figure 4. Calibration curves for unidirectional capacitor with core flow field,
I
0.0
02
,
i
0./,
,
I
0.6
,
I
0.B
1.0
ACTUAL VOID FRACTION Figure 6. Calibration curve of the parallel-plate capacitor with air-paraffin wax and core flow simulation.
Improving the Accuracy of Capacitance Method
325
Table 3. A Comparison of the Five Capacitor Types
Average Capacitance C 1 (ce = 1) CO (a = (pF) (pF)
Test-Section Material
Capacitor T y p e Parallel plates Strip
Perspex Glass
368.5 598 598 675 601 509 2.76 2.76 12.5 12.5 12.85
Perspex Ring Unidirectional
Perspex Perspex
Double helix
Perspex
Sensitivity ( 6C / 6a ) (pF)
O)
399.5 665 662 700 678 533 3.12 2.87 16.5 14.2 16.4
Flow-Simulation Materials
31.0 72.0 60.0 25.0 77.0 24.0 0.36 0.11 4.0 1.7 3.55
with the time trace recorded in two-phase flow pipe2a~ lines. 3. The effects of using other materials of capacitors on 24.0 void fraction m e a s u r e m e n t - - f o r example, tantalum foils, polyester dielectrics, polystyrene foils, silvered r i o 20.0 mica, and metallized paper. 4. The influence of irregularities in the actual two-phase p-, flow patterns on the accuracy of void fraction measure- l a d 16.0 ment by capacitors. 12.0
L,d=as
Air-paraffin Air-wood Air-paraffin Air-Glass Air-wood Air-paraffin Air-wood Air-paraffin Air-wood Air-paraffin Air-wood
.
1~=1.0
.
.
.
Flow Pattern
wax
Core Core Core Core Annular Core Core Core Core Core Annular
wax
wax wax wax
.
.
.
.
.~,2
W OC
NOMENCLATURE
a,b,d-h C C* Co
-- 7
0
constants defined by Eq. (2), m total capacitance, F relative capacitance, dimensionless capacitance at a = 0, F
0
I
I
~
I
~.0
=" 0)
0~
0'2
[
d~ d~ d~ 0 ACTUAL VOID F R A C T I O N
0.'3
~
.
d.9
1.0
Figure 8. Experimental optimization of the L / D ratio for the strip-type capacitor.
14 u_ ta
L i I i
12
'-~ 65C tJ
i
Z
10
~J
\
1 \
0
\
h*
\
~
575
0.0
,
n
n
m
0.2
0./*
0.6
0.8
1.0
ACTUAL VOID FRACTION
Figure 7. Calibration curves of the strip-type capacitor. Perspex test section: air-glass, core flow (0). Glass test section: core flow (m) air-paraffin wax, (©) air-wood, core flow (*) air-wood annular flow.
,v/
,~---E.~perimentot results using
Chun ¢ Sung IS:]equatFons(crosses)
k
k
60o
\
\~
x
/
~Experimentol results usinQ present equations(g)&(10}
(circles)
0 O.0
0.1
0.2
03 0.4 0.5 0.6 0.7 ACTUAL VOID FRACTION
0.8
0.9
1.0
Figure 9. Experimental validation of the theoretical results for the strip-type capacitor and air-paraffin wax core flow simulation.
326
A . A . Kendoush and Z. A. Sarkis
70
60
~
~,, A~ \
50
A : CHUN& SUNG(53 EQUATIONS B : PRESENT EQUATIONS(g)&(t0} C : SHIELDED CAPACITOR
nr
L~ I.a.I
4O
z
spacing b e t w e e n the ends of the two electrodes, m
O/
void fraction, dimensionless permittivities of fluids 1 and 2, C 2 / ( N m-) dielectric constant, dimensionless
Greek Symbols E 1, E 2
eR
30
REFERENCES
ILl n,"
.-e 20 10 00
i
0.0
0'.1
0.2
i
|
?o
0.3 0.4 0.5 0.6 0.7 ACTUAL VOID FRACTION
v
0.8
i
0.9
Figure 10. Experimental results of the parallel-plate capacitor and air-paraffin wax core flow simulation.
CI Cl, C21, C22, C23, C 3
D d L
c a p a c i t a n c e at a = 1, F constants defined by Eq. (4), C 2 / ( N m) o u t e r d i a m e t e r o f test section, m o u t e r d i a m e t e r of fluid I in the test section, m axial e l e c t r o d e length, m
1.0
1. Kendoush, A. A., A Comparative Study of the Various Nuclear Radiations Used for Void Fraction Measurements, Nucl. Eng. Des. 137, 249-257, 1992. 2. Duckier, A. E., and Bergelin, O. P., Characteristics of Flow in Falling Liquid Films, Chem. Eng. Prog. 48, 557-563, 1952. 3. Tailby, S. R., and Portalski, S., The Hydrodynamics of Liquid Films Flow on a Vertical Surface, Trans. Inst. Chem. Eng., 38, 324-330, 1960. 4. Abouelwafa, S., and Kendall, J. M., The Use of Capacitance Sensors for Phase Percentage Determination in Multiphase Pipelines, IEEE Trans. Instrum. Measure, IM-29, 24-29, 1980. 5. Chun, M.-H., and Sung, C.-K., Parametric Effects on the Void Fraction Measurement by Capacitance Transducers, Int. J. Multiphase Flow 12, 627 640, 1986. 6. Fink, D. G., and Carroll, J. M., Standard Handbook for Electrical Engineers, McGraw-Hill, New York, 1968.
Received September 6, 1994; revised March 6, 1995