- Email: [email protected]
The turbine meter applied to void fraction determination in two-phase flow
246
P. A. Mark et al - The turbine meter applied to void fraction determination in two-phase flow
The turbine meter applied to void fraction determination in two-phase flow P. A. MARK, M. W. J O H N S O N , J. L. SPROSTON and B. C. M I L L I N G T O N A n e w approach to analysing the pulse output information from a standard turbine meter in two-phase liquid/gas flows is presented. After suitable calibration, the meter will register the presence o f gas, with an accurate indication o f void fraction up to 20%, and provide a measure o f the liquid flowrate. The single-phase performance o f the meter remains unaffected.
Keywords: turbine meter, void fraction, two-phase flow, liquid flowrate
Introduction
Experimental arrangement
The two-phase flow of a liquid and a gas occurs in many industrial situations either intentionally or unintentionally, examples being the chemical process industry and in crude oil production. In custody transfer, where a high accuracy in metering the liquid flowrate is required, the standard technique is to separate the two phases, the single-phase liquid then being metered using existing technology ~. However, the provision of separating devices not only occupies significant and often valuable space, but also has a high financial cost. In other cases, the operator is more concerned with simply being aware of the presence of the gas phase, whilst still obtaining a reasonable indication of liquid flowrate. In an attempt to overcome the need for separation, the development of a two-phase flowmeter was sought-'. Some of the existing meters have been tested to a greater or lesser extent in two-phase flows. In the main there are two outcomes: either the meter is unsuitable for use in two-phase flow or the meter produces repeatable results but the void fraction must be known to correct the output. One such meter that falls into this latter category is the turbine meter. Application of the standard turbine meter in twophase (liquid/gas) flow conditions, but without correction for void fraction, leads to an error in metering the liquid flowrate, the magnitude and the sign of the error being dependent on the flow conditions and the type of meter used. The operator has no way of detecting the presence of gas and thereby correcting the meter output without the aid of a void determination device such as those employing capacitance or y-ray attenuation techniques. The development of a meter that registers not only flowrate, but also the fraction of gas-phase present in the two-phase flow represents a major step towards satisfactory measurement of two-phase flows. This paper is concerned with investigating how the output signal from a standard turbine meter can be used to achieve this goal. P. A. M., M. W. J. and J. L. S. are at the Departmentof Mechanical Engineering, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK. B. C M. is at the National Engineering Laboratory, East Kilbride, Glasgow G75 OQU, UK.
0955-5986/90/050246-07
The experiments were conducted in the horizontal two-phase water/air flow facility constructed at the University of Liverpool under a DTI EMRA contract. The system is shown schematically in Figure 1. Water is supplied from a large roof-top tank of nominally constant head generating a static pressure in the working section of 3.5 bar. The working section is of 4 inch diameter plastic pipework, approximately 15 m in length. The water flowrate is measured using a regularly calibrated 4 inch turbine meter. Air injection occurs downstream from the reference meter, the air flow being metered through a bank of rotameters. The two-phase flow is allowed to develop into its naturally occurring flow pattern over 60 pipe diameters before entering the test meter. The rig operating pressure is recorded immediately upstream of the test meter and is used to correct the rotameter readings for different rig conditions by using the procedure presented by Millington and King 3. Perspex pipe sections are used upstream and downstream of the test meter to allow observation of the flow patterns and of the phase distribution. The flow leaves the working section and passes through a diverter valve either directly to the sump or into the gravimetric facility, the primary standard for the laboratory. Water from the sump is pumped back to the supply tank to maintain a constant head. Pulse information from the reference and test meters together with rig pressure conditions are logged automatically on an Opus PC V computer, whilst the rotameter readings are input manually. The three meters investigated here were 4 inch turbine meters with eight flat constant-angle blades. The only geometrical difference between the three meters was the blade angle, which was 20, 30 and 40 ° to the axis of rotation.
Signal analysis The technique often used to sense rotation of the turbine rotor is that of variable reluctance in which the passage of a magnetic insert at the blade tip past an external pick-up coil generates an AC voltage in the external pick-up circuit. Normally, the number of © 1990 Butterworth-HeinemannLtd
Flow Meas. Instrum.
Vol 1 October 1990
247
Supply tank
Gravimetric facility
-~ I
Data logger
I
I
_
j 'i" li
Air injection
I I
I
I I
D,
I I
IiPressure i transducer
'o I
I
Reference meter
Test
meter
Flow straightener
Pump
,, [
Sump
Figure 1 Schematic of the test facility
voltage peaks or pulses over a given period of time are counted to obtain the output frequency. By using the meter factor determined from the manufacturer's calibration, the pulse output frequency then gives the volume flowrate. This present study analyses the meter output signal in a different fashion. The fluctuating AC voltage from the meter is amplified and digitized, the original sine wave being modified in the process to a square wave. A machine code program compares each reading with a preset threshold level, which is set approximately midway between the low and high square wave voltage levels, as shown in Figure 2. Each time this threshold level is passed from below, marking the start of a pulse, a count of the number of times the program passes through a loop of known duration commences. This continues until the threshold level is again crossed from below, indicating the start of the next voltage pulse. The counts between 4096
I
each pair of pulses is thus used to compute the duration and the instantaneous rotor frequency. At present 30000 sequential durations can be recorded, covering a minimum recording period of 25 s for the 4 inch meter for the current maximum flowrate of 60 I s-7. Under single-phase steady flow conditions there is a degree of scatter in the instantaneous frequencies caused by irregularities in the spacing of the magnetic inserts and the resolution of the pulse duration algorithm. This is effectively removed by using a Butterworth low pass filter with a 24 dB attenuation/octave set with a - 3 dB point of 48 readings (i.e. the duration for one complete revolution of the rotor). Currently the average meter frequency and the RMS of the duration between pulses are computed. For a given set of flow conditions the RMS value of the duration between pulses is multiplied by the average meter frequency to give a value termed the signal turbulence. The turbulence level is an indication of the amplitude of rotor frequency changes occurring during the measuring period.
¢D
.= o
2048
Results
Threshold
I'leve
I
._= E3
T2 Time
Figure 2 5etting of the pulse threshold level: (I) onset of initial pulse; (2) onset of a second pulse; T2 - T1, duration between pulses (Hz-1)
The instantaneous rotor angular velocities were recorded for each of the test meters over a water flow range of 5 to 60 Is -~ and for void fractions up to 25%. The flow patterns generated under such conditions were unsteady stratified slug flow, stratified bubbly flow and a transitional pattern. Stratified slug flow occurred at liquid flowrates of between 5 and 20 Is -1 and for all void fractions considered. It consisted of slugs of gas occupying up to 50% of the flow area,
248
P. A. Mark et al - The turbine meter applied to void fraction determination in two-phase flow i
separated by plugs of liquid. For liquid flows of between 30 and 60 Is -~ and, again, for all void fractions considered, stratified bubbly flow occurred. This regime-consisted of a mass of small gas bubbles dispersed in the liquid phase, buoyancy effects resulting in the bubbles congregating at the top of the pipe. The flow was steady. A transitional pattern occurred for liquid flows of between 20 and 30Is -~, exhibiting traits of the two main patterns. Examples of the fluctuating duration between pulses in two-phase flow conditions are shown in Figures 3 and 4. Subsequent analysis of each signal gives the signal turbulence, which is plotted against reference meter frequency for each of the test meters (Figures 5, 6 and 7). Generally, twenty seconds of data was recorded
i
1
95 '7; 1
. ....
¢'";'
94 "" E
93
E t-
=
91
I
90500
6(~0
I
700 800 Pulse number
I
900
1000
Figure 4 Duration between pulses versus pulse number recorded under bubbly flow conditions with the 30 ° rotor: void fraction, 5%; liquid flow rate, 53 Is -1
46
44 T
at each flow condition to achieve a good time average. However, it was clear when analysing the data that reasonable results could be obtained with much shorter data collection periods.
42
i=
40
..T
Discussion 38
36
I 600
500
I
t
700 800 Pulse number
Figure 3 shows a sample of low pass filtered data obtained from the 30° rotor, time between pulses plotted against pulse number. The flow pattern occurring during data collection was that of unsteady, stratified slug flow. The plot consists of a series of quite sharp peaks separated by relatively flat plateaux. The ascending face of the peaks represents increasing time between pulses, i.e. rotor deceleration, whilst the descending faces represent rotor acceleration. These
t
900
1000
Figure 3 Duration between pulses versus pulse number recorded under slug flow conditions with the 30 ° rotor: void fraction, 5%; liquid flowrate, 12 Is -~
0.20
0
0
Void fraction (%)
0
•
+
0
5
10
[] 15
0.15
X
× []
0.10 }-
[]
X 20 25
©
X
[]
[]
X X
0.05
[] +
" -t-
0
I 200
+
I • 400
+ ]0
60O
Meter frequency (Hz)
Figure 5 Signal turbulence versus reference meter frequency for the 30 ° rotor
8O0
1000
Flow Meas. Instrum.
249
Vol 1 October 1990
0.25 Void fraction (%)
0.20
0
8
0
5
~= 10
D 15 X 20 0 25
0 0.15
•
+
×
X X D
F-
0.10
E3
X
[]
o 0.05
+++ •
•
•
+ @
+
+
I
I
I
20O
400
600
+
I 800
1000
Meter frequency (Hz)
Figure 6 Signal turbulence versus reference meter frequency for the 20 ° rotor
0.08 Void fraction (%) 10
•
0.06
0.04 @
0.02
0
I
I
I
1
1
200
400
600
800
1000
1200
Meter frequency (Hz)
Figure 7 Signal turbulence versus reference meter frequency for the 40 ° rotor
peaks occur as each gas slug passes through the rotor, thus reducing the driving torque generated by the rotor because of the low density of the gas phase. Since the rotor speed is proportional to driving torque, this results in the deceleration of the rotor. The rate of deceleration is dependent on slug shape, fluid densities, frictional losses and rotor inertia. When the gas slug is replaced by the following liquid plug the rotor quickly accelerates back to its original speed4. As long as the rotor remains within a liquid plug the time between pulses will remain constant: hence the pla-
teaux in Figure 3. As the liquid flow rate was increased the flow pattern changed to bubbly stratified flow. Since the flow is essentially steady the peaks and plateaux generated under slug flow conditions do not occur, as shown in Figure 4, but the signal does oscillate about some mean value. The turbulence levels calculated using the procedure presented in the preceding section on signal analysis and shown in Figures 5-7 indicate that a unique turbulence characteristic is developed for each void fraction over the operating range of each meter.
250
P. A. Mark et al - The turbine meter applied to void fraction determination in two-phase flow
Since the response is unique and repeatable this suggests that, provided the meter were to be calibrated over a range of two-phase flow conditions, the turbulence signal could be used to obtain void fraction. This would, however, require significant calibration time to cover the full range of two-phase flow conditions. From Figures 5, 6 and 7 it is apparent that the form of the turbulence characteristic is similar in all cases. The turbulence rises quickly to a peak value and then gradually reduces. The form of the turbulence characteristic is dependent on the flow pattern entering the rotor. At low liquid flowrates when slug flow occurs the speed fluctuations are large because of the changing driving torque, discussed above, and hence the turbulence level is high. At higher liquid flows, but with slug flow still dominant, the period for which the gas slug influences the rotor is reduced. Therefore the time over which rotor deceleration occurs is also reduced. Since the rate of rotor deceleration is nominally constant this results in a decrease in turbulence level. As the liquid flowrate increases the flow pattern gradually changes to bubbly flow and since this is a steady flow regime with a relatively constant liquid/gas distribution, the speed fluctuations are smaller and so the turbulence level is reduced. As well as the form similarity, the level of signal turbulence appears to be dependent on void fraction. For the 30 ° rotor the turbulence was notionally 'nondimensionalized' by dividing by void fraction. These non-dimensional turbulence (NDT) values are shown plotted against reference meter frequency in Figure 8. It is clear from this that the data collapses reasonably well onto a single curve where the NDT is a function solely of the meter frequency. This suggests that, for any meter, calibration need only be made at one void fraction in order to determine the form of the meter turbulence characteristic. This would reduce the meter calibration time to little more than that for a singlephase calibration. Non-dimensionalizing the data for the 20 and 40 ° rotors produces single curves when plotted in a similar
manner. By plotting all of the data for the three meters on a single graph of NDT against reference meter frequency (water flowrate), as in Figure 9, it is observed that all the data falls more or less on a single characteristic. This suggests that the turbulence level in the duration between pulses is purely a function of the flow pattern and phase distribution, with the meter geometry having little, if any, influence. A fourth-order polynomial equation is fitted to the NDT characteristic with a correlation of 0.944 and a standard deviation error of 0.067. Now that the meter turbulence has been obtained the meter's performance in determining void fraction can be assessed. This is undertaken in the following manner. The RMS of duration between pulses is determined for a short period and then multiplied by the average meter pulse frequency to give the measured turbulence. Using the average frequency in the NDT characteristic equation gives the NDT for that given flow condition and by simply dividing the measured turbulence by the NDT the void fraction can be found. Figure 10 indicates the performance of the 30 ° rotor in determining void fraction when operating at known void fractions of 5 and 10%. The agreement is good, particularly at low liquid flowrates, with rather less agreement at the higher flowrates. This reduction in accuracy is felt to be due to the different flow pattern existing at the higher flowrates. At low liquid flowrates, when slug flow occurs, the turbulence levels for each void fraction considered are well separated, as shown by Figures 5-7. Scatter occurring in the signal is small compared with this separation. However, at higher flowrates when bubbly flow occurs the separation is reduced to a level comparable with the scatter level. Hence the accuracy at these higher flows is reduced. Scatter of the data about the equation fitted to the NDT characteristic, shown in Figure 9, will introduce errors when using the equation to determine void fraction. This scatter may be reduced by using an alternative algorithm to RMS levels (see the later
1.0
Void fraction (%) 0.8
x
x [] l-a Z
0.6
x
•
•
10
*
15
[] 2O X 25
*
[]
5
+
D+
t;× [] ,%
0.4
-¢ 0.2
+
0
i 200
L 400
I 600
I 800
Meter frequency (Hz)
Figure 8 Non-dimensiona/ized turbu/ence versus reference meter frequency for the 30 ° rotor
1000
Flow Meas. Instrum.
251
Vol 1 October 1990
1.0
Rotor blade angle (deg) • 3O + 20 ~= 40
0.8
•+
*4-
+•
0.6
•
I-~3 Z
-t-o
+
+
+
,+
0.4
+
4- ~
•
•
~+*o+0 | 0.2
+
+
+
I 200
0
I 400
+
•
I 600
+
+ I
I 800
1000
1200
Reference meter frequency (Hz)
Figure 9 Non-dimensionalized turbulence versus reference meter frequency for all rotors 20 18
+ []
Actual void
Measured void
16 14 A v
g_
[]
12 10
E3 ,~
[]
[]
[]
E]
,•
+ []
0
>
8
D
+
+
+
+
6 4
4-
2 I
I
I
I
I
200
400
600
800
I~0
1200
Meter frequency (Hz)
Figure 10 Performance of a 30 ° rotor in predicting void traction
section on future work). Alternatively, if the scatter is due to random effects, then by taking more readings at a given set of conditions the uncertainty should be reduced. Conclusions
[ ] Fluctuations in the time between voltage pulses occur when operating a turbine meter in two-phase liquid/gas flows. This implies that rotor speed changes occur because of the presence of the second phase. [ ] Signal turbulence is a function solely of flow
conditions. [ ] At any liquid flowrate the level of signal turbulence is directly proportional to the void fraction. [ ] Because of the nature of the turbulence characteristic the signal output from a standard turbine meter can be used to give an indication of both liquid flowrate and void fraction, after calibration. Future work
Only one group of turbine meters has been tested here and although the turbulence level of the duration between pulses was found to be independent of blade
252
P. A. Mark et al - The turbine meter applied to void fraction determination in two-phase flow
angle, it is important to determine whether other changes in meter geometry will influence the void fraction calibration curve, The rotor inertia and retarding torque are considered likely to be of particular importance. The choice of the RMS value to characterize the fluctuations in rotor speed is simple and, as shown in the current work, effective. However, improved schemes are possible by considering the physics of rotor response to a slug. This topic has already been described by Mark et al. 4. In this work the operating fluids have been limited to water and air. The effect of liquid phase density and viscosity on the meter's performance must be considered. Such a study is presently being undertaken at the National Engineering Laboratory, East Kilbride, using kerosine and air.
Acknowledgment The work presented in this paper was done by the
authors under an Extra Mural Research Award (EMRA) contract with the Department of Trade and Industry.
References 1 King, N. W. 'Methods of separating multi-phase flows', In Multi-Phase Flow in Pipeline Systems (Ed. N. W. King), Paper 12 (1990) 2 Kinghorn, F. C. and McHugh, A. 'The performance of turbine meters in two component gas/liquid flow', In Flow: Its Measurement and Control in Science and Industry, St. Louise, Missouri, March 1981, pp 471-492, ISA, Triangle Park, USA 3 Millinglon, B. C. and King, N. W. 'The performance of a turbine meter in gas/liquid flow with upstream flow conditioning', In Proc. Int. Conf. on Flow Measurement in the Mid 80s, Glasgow, 9-12 June 1986, Vol. 1, paper 2.3, N.E.L. 4 Mark, P. A., Sproston, J. L. and Johnson, M. W. 'Theoretical and experimental studies of turbine meters in twophase flows', In Int. Conf. on Basic Principles and Industrial Applications of Multiphase Flow, London, 24-25 April 1990, IBC Technical Services Ltd
P. A. Mark et al - The turbine meter applied to void fraction determination in two-phase flow
The turbine meter applied to void fraction determination in two-phase flow P. A. MARK, M. W. J O H N S O N , J. L. SPROSTON and B. C. M I L L I N G T O N A n e w approach to analysing the pulse output information from a standard turbine meter in two-phase liquid/gas flows is presented. After suitable calibration, the meter will register the presence o f gas, with an accurate indication o f void fraction up to 20%, and provide a measure o f the liquid flowrate. The single-phase performance o f the meter remains unaffected.
Keywords: turbine meter, void fraction, two-phase flow, liquid flowrate
Introduction
Experimental arrangement
The two-phase flow of a liquid and a gas occurs in many industrial situations either intentionally or unintentionally, examples being the chemical process industry and in crude oil production. In custody transfer, where a high accuracy in metering the liquid flowrate is required, the standard technique is to separate the two phases, the single-phase liquid then being metered using existing technology ~. However, the provision of separating devices not only occupies significant and often valuable space, but also has a high financial cost. In other cases, the operator is more concerned with simply being aware of the presence of the gas phase, whilst still obtaining a reasonable indication of liquid flowrate. In an attempt to overcome the need for separation, the development of a two-phase flowmeter was sought-'. Some of the existing meters have been tested to a greater or lesser extent in two-phase flows. In the main there are two outcomes: either the meter is unsuitable for use in two-phase flow or the meter produces repeatable results but the void fraction must be known to correct the output. One such meter that falls into this latter category is the turbine meter. Application of the standard turbine meter in twophase (liquid/gas) flow conditions, but without correction for void fraction, leads to an error in metering the liquid flowrate, the magnitude and the sign of the error being dependent on the flow conditions and the type of meter used. The operator has no way of detecting the presence of gas and thereby correcting the meter output without the aid of a void determination device such as those employing capacitance or y-ray attenuation techniques. The development of a meter that registers not only flowrate, but also the fraction of gas-phase present in the two-phase flow represents a major step towards satisfactory measurement of two-phase flows. This paper is concerned with investigating how the output signal from a standard turbine meter can be used to achieve this goal. P. A. M., M. W. J. and J. L. S. are at the Departmentof Mechanical Engineering, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK. B. C M. is at the National Engineering Laboratory, East Kilbride, Glasgow G75 OQU, UK.
0955-5986/90/050246-07
The experiments were conducted in the horizontal two-phase water/air flow facility constructed at the University of Liverpool under a DTI EMRA contract. The system is shown schematically in Figure 1. Water is supplied from a large roof-top tank of nominally constant head generating a static pressure in the working section of 3.5 bar. The working section is of 4 inch diameter plastic pipework, approximately 15 m in length. The water flowrate is measured using a regularly calibrated 4 inch turbine meter. Air injection occurs downstream from the reference meter, the air flow being metered through a bank of rotameters. The two-phase flow is allowed to develop into its naturally occurring flow pattern over 60 pipe diameters before entering the test meter. The rig operating pressure is recorded immediately upstream of the test meter and is used to correct the rotameter readings for different rig conditions by using the procedure presented by Millington and King 3. Perspex pipe sections are used upstream and downstream of the test meter to allow observation of the flow patterns and of the phase distribution. The flow leaves the working section and passes through a diverter valve either directly to the sump or into the gravimetric facility, the primary standard for the laboratory. Water from the sump is pumped back to the supply tank to maintain a constant head. Pulse information from the reference and test meters together with rig pressure conditions are logged automatically on an Opus PC V computer, whilst the rotameter readings are input manually. The three meters investigated here were 4 inch turbine meters with eight flat constant-angle blades. The only geometrical difference between the three meters was the blade angle, which was 20, 30 and 40 ° to the axis of rotation.
Signal analysis The technique often used to sense rotation of the turbine rotor is that of variable reluctance in which the passage of a magnetic insert at the blade tip past an external pick-up coil generates an AC voltage in the external pick-up circuit. Normally, the number of © 1990 Butterworth-HeinemannLtd
Flow Meas. Instrum.
Vol 1 October 1990
247
Supply tank
Gravimetric facility
-~ I
Data logger
I
I
_
j 'i" li
Air injection
I I
I
I I
D,
I I
IiPressure i transducer
'o I
I
Reference meter
Test
meter
Flow straightener
Pump
,, [
Sump
Figure 1 Schematic of the test facility
voltage peaks or pulses over a given period of time are counted to obtain the output frequency. By using the meter factor determined from the manufacturer's calibration, the pulse output frequency then gives the volume flowrate. This present study analyses the meter output signal in a different fashion. The fluctuating AC voltage from the meter is amplified and digitized, the original sine wave being modified in the process to a square wave. A machine code program compares each reading with a preset threshold level, which is set approximately midway between the low and high square wave voltage levels, as shown in Figure 2. Each time this threshold level is passed from below, marking the start of a pulse, a count of the number of times the program passes through a loop of known duration commences. This continues until the threshold level is again crossed from below, indicating the start of the next voltage pulse. The counts between 4096
I
each pair of pulses is thus used to compute the duration and the instantaneous rotor frequency. At present 30000 sequential durations can be recorded, covering a minimum recording period of 25 s for the 4 inch meter for the current maximum flowrate of 60 I s-7. Under single-phase steady flow conditions there is a degree of scatter in the instantaneous frequencies caused by irregularities in the spacing of the magnetic inserts and the resolution of the pulse duration algorithm. This is effectively removed by using a Butterworth low pass filter with a 24 dB attenuation/octave set with a - 3 dB point of 48 readings (i.e. the duration for one complete revolution of the rotor). Currently the average meter frequency and the RMS of the duration between pulses are computed. For a given set of flow conditions the RMS value of the duration between pulses is multiplied by the average meter frequency to give a value termed the signal turbulence. The turbulence level is an indication of the amplitude of rotor frequency changes occurring during the measuring period.
¢D
.= o
2048
Results
Threshold
I'leve
I
._= E3
T2 Time
Figure 2 5etting of the pulse threshold level: (I) onset of initial pulse; (2) onset of a second pulse; T2 - T1, duration between pulses (Hz-1)
The instantaneous rotor angular velocities were recorded for each of the test meters over a water flow range of 5 to 60 Is -~ and for void fractions up to 25%. The flow patterns generated under such conditions were unsteady stratified slug flow, stratified bubbly flow and a transitional pattern. Stratified slug flow occurred at liquid flowrates of between 5 and 20 Is -1 and for all void fractions considered. It consisted of slugs of gas occupying up to 50% of the flow area,
248
P. A. Mark et al - The turbine meter applied to void fraction determination in two-phase flow i
separated by plugs of liquid. For liquid flows of between 30 and 60 Is -~ and, again, for all void fractions considered, stratified bubbly flow occurred. This regime-consisted of a mass of small gas bubbles dispersed in the liquid phase, buoyancy effects resulting in the bubbles congregating at the top of the pipe. The flow was steady. A transitional pattern occurred for liquid flows of between 20 and 30Is -~, exhibiting traits of the two main patterns. Examples of the fluctuating duration between pulses in two-phase flow conditions are shown in Figures 3 and 4. Subsequent analysis of each signal gives the signal turbulence, which is plotted against reference meter frequency for each of the test meters (Figures 5, 6 and 7). Generally, twenty seconds of data was recorded
i
1
95 '7; 1
. ....
¢'";'
94 "" E
93
E t-
=
91
I
90500
6(~0
I
700 800 Pulse number
I
900
1000
Figure 4 Duration between pulses versus pulse number recorded under bubbly flow conditions with the 30 ° rotor: void fraction, 5%; liquid flow rate, 53 Is -1
46
44 T
at each flow condition to achieve a good time average. However, it was clear when analysing the data that reasonable results could be obtained with much shorter data collection periods.
42
i=
40
..T
Discussion 38
36
I 600
500
I
t
700 800 Pulse number
Figure 3 shows a sample of low pass filtered data obtained from the 30° rotor, time between pulses plotted against pulse number. The flow pattern occurring during data collection was that of unsteady, stratified slug flow. The plot consists of a series of quite sharp peaks separated by relatively flat plateaux. The ascending face of the peaks represents increasing time between pulses, i.e. rotor deceleration, whilst the descending faces represent rotor acceleration. These
t
900
1000
Figure 3 Duration between pulses versus pulse number recorded under slug flow conditions with the 30 ° rotor: void fraction, 5%; liquid flowrate, 12 Is -~
0.20
0
0
Void fraction (%)
0
•
+
0
5
10
[] 15
0.15
X
× []
0.10 }-
[]
X 20 25
©
X
[]
[]
X X
0.05
[] +
" -t-
0
I 200
+
I • 400
+ ]0
60O
Meter frequency (Hz)
Figure 5 Signal turbulence versus reference meter frequency for the 30 ° rotor
8O0
1000
Flow Meas. Instrum.
249
Vol 1 October 1990
0.25 Void fraction (%)
0.20
0
8
0
5
~= 10
D 15 X 20 0 25
0 0.15
•
+
×
X X D
F-
0.10
E3
X
[]
o 0.05
+++ •
•
•
+ @
+
+
I
I
I
20O
400
600
+
I 800
1000
Meter frequency (Hz)
Figure 6 Signal turbulence versus reference meter frequency for the 20 ° rotor
0.08 Void fraction (%) 10
•
0.06
0.04 @
0.02
0
I
I
I
1
1
200
400
600
800
1000
1200
Meter frequency (Hz)
Figure 7 Signal turbulence versus reference meter frequency for the 40 ° rotor
peaks occur as each gas slug passes through the rotor, thus reducing the driving torque generated by the rotor because of the low density of the gas phase. Since the rotor speed is proportional to driving torque, this results in the deceleration of the rotor. The rate of deceleration is dependent on slug shape, fluid densities, frictional losses and rotor inertia. When the gas slug is replaced by the following liquid plug the rotor quickly accelerates back to its original speed4. As long as the rotor remains within a liquid plug the time between pulses will remain constant: hence the pla-
teaux in Figure 3. As the liquid flow rate was increased the flow pattern changed to bubbly stratified flow. Since the flow is essentially steady the peaks and plateaux generated under slug flow conditions do not occur, as shown in Figure 4, but the signal does oscillate about some mean value. The turbulence levels calculated using the procedure presented in the preceding section on signal analysis and shown in Figures 5-7 indicate that a unique turbulence characteristic is developed for each void fraction over the operating range of each meter.
250
P. A. Mark et al - The turbine meter applied to void fraction determination in two-phase flow
Since the response is unique and repeatable this suggests that, provided the meter were to be calibrated over a range of two-phase flow conditions, the turbulence signal could be used to obtain void fraction. This would, however, require significant calibration time to cover the full range of two-phase flow conditions. From Figures 5, 6 and 7 it is apparent that the form of the turbulence characteristic is similar in all cases. The turbulence rises quickly to a peak value and then gradually reduces. The form of the turbulence characteristic is dependent on the flow pattern entering the rotor. At low liquid flowrates when slug flow occurs the speed fluctuations are large because of the changing driving torque, discussed above, and hence the turbulence level is high. At higher liquid flows, but with slug flow still dominant, the period for which the gas slug influences the rotor is reduced. Therefore the time over which rotor deceleration occurs is also reduced. Since the rate of rotor deceleration is nominally constant this results in a decrease in turbulence level. As the liquid flowrate increases the flow pattern gradually changes to bubbly flow and since this is a steady flow regime with a relatively constant liquid/gas distribution, the speed fluctuations are smaller and so the turbulence level is reduced. As well as the form similarity, the level of signal turbulence appears to be dependent on void fraction. For the 30 ° rotor the turbulence was notionally 'nondimensionalized' by dividing by void fraction. These non-dimensional turbulence (NDT) values are shown plotted against reference meter frequency in Figure 8. It is clear from this that the data collapses reasonably well onto a single curve where the NDT is a function solely of the meter frequency. This suggests that, for any meter, calibration need only be made at one void fraction in order to determine the form of the meter turbulence characteristic. This would reduce the meter calibration time to little more than that for a singlephase calibration. Non-dimensionalizing the data for the 20 and 40 ° rotors produces single curves when plotted in a similar
manner. By plotting all of the data for the three meters on a single graph of NDT against reference meter frequency (water flowrate), as in Figure 9, it is observed that all the data falls more or less on a single characteristic. This suggests that the turbulence level in the duration between pulses is purely a function of the flow pattern and phase distribution, with the meter geometry having little, if any, influence. A fourth-order polynomial equation is fitted to the NDT characteristic with a correlation of 0.944 and a standard deviation error of 0.067. Now that the meter turbulence has been obtained the meter's performance in determining void fraction can be assessed. This is undertaken in the following manner. The RMS of duration between pulses is determined for a short period and then multiplied by the average meter pulse frequency to give the measured turbulence. Using the average frequency in the NDT characteristic equation gives the NDT for that given flow condition and by simply dividing the measured turbulence by the NDT the void fraction can be found. Figure 10 indicates the performance of the 30 ° rotor in determining void fraction when operating at known void fractions of 5 and 10%. The agreement is good, particularly at low liquid flowrates, with rather less agreement at the higher flowrates. This reduction in accuracy is felt to be due to the different flow pattern existing at the higher flowrates. At low liquid flowrates, when slug flow occurs, the turbulence levels for each void fraction considered are well separated, as shown by Figures 5-7. Scatter occurring in the signal is small compared with this separation. However, at higher flowrates when bubbly flow occurs the separation is reduced to a level comparable with the scatter level. Hence the accuracy at these higher flows is reduced. Scatter of the data about the equation fitted to the NDT characteristic, shown in Figure 9, will introduce errors when using the equation to determine void fraction. This scatter may be reduced by using an alternative algorithm to RMS levels (see the later
1.0
Void fraction (%) 0.8
x
x [] l-a Z
0.6
x
•
•
10
*
15
[] 2O X 25
*
[]
5
+
D+
t;× [] ,%
0.4
-¢ 0.2
+
0
i 200
L 400
I 600
I 800
Meter frequency (Hz)
Figure 8 Non-dimensiona/ized turbu/ence versus reference meter frequency for the 30 ° rotor
1000
Flow Meas. Instrum.
251
Vol 1 October 1990
1.0
Rotor blade angle (deg) • 3O + 20 ~= 40
0.8
•+
*4-
+•
0.6
•
I-~3 Z
-t-o
+
+
+
,+
0.4
+
4- ~
•
•
~+*o+0 | 0.2
+
+
+
I 200
0
I 400
+
•
I 600
+
+ I
I 800
1000
1200
Reference meter frequency (Hz)
Figure 9 Non-dimensionalized turbulence versus reference meter frequency for all rotors 20 18
+ []
Actual void
Measured void
16 14 A v
g_
[]
12 10
E3 ,~
[]
[]
[]
E]
,•
+ []
0
>
8
D
+
+
+
+
6 4
4-
2 I
I
I
I
I
200
400
600
800
I~0
1200
Meter frequency (Hz)
Figure 10 Performance of a 30 ° rotor in predicting void traction
section on future work). Alternatively, if the scatter is due to random effects, then by taking more readings at a given set of conditions the uncertainty should be reduced. Conclusions
[ ] Fluctuations in the time between voltage pulses occur when operating a turbine meter in two-phase liquid/gas flows. This implies that rotor speed changes occur because of the presence of the second phase. [ ] Signal turbulence is a function solely of flow
conditions. [ ] At any liquid flowrate the level of signal turbulence is directly proportional to the void fraction. [ ] Because of the nature of the turbulence characteristic the signal output from a standard turbine meter can be used to give an indication of both liquid flowrate and void fraction, after calibration. Future work
Only one group of turbine meters has been tested here and although the turbulence level of the duration between pulses was found to be independent of blade
252
P. A. Mark et al - The turbine meter applied to void fraction determination in two-phase flow
angle, it is important to determine whether other changes in meter geometry will influence the void fraction calibration curve, The rotor inertia and retarding torque are considered likely to be of particular importance. The choice of the RMS value to characterize the fluctuations in rotor speed is simple and, as shown in the current work, effective. However, improved schemes are possible by considering the physics of rotor response to a slug. This topic has already been described by Mark et al. 4. In this work the operating fluids have been limited to water and air. The effect of liquid phase density and viscosity on the meter's performance must be considered. Such a study is presently being undertaken at the National Engineering Laboratory, East Kilbride, using kerosine and air.
Acknowledgment The work presented in this paper was done by the
authors under an Extra Mural Research Award (EMRA) contract with the Department of Trade and Industry.
References 1 King, N. W. 'Methods of separating multi-phase flows', In Multi-Phase Flow in Pipeline Systems (Ed. N. W. King), Paper 12 (1990) 2 Kinghorn, F. C. and McHugh, A. 'The performance of turbine meters in two component gas/liquid flow', In Flow: Its Measurement and Control in Science and Industry, St. Louise, Missouri, March 1981, pp 471-492, ISA, Triangle Park, USA 3 Millinglon, B. C. and King, N. W. 'The performance of a turbine meter in gas/liquid flow with upstream flow conditioning', In Proc. Int. Conf. on Flow Measurement in the Mid 80s, Glasgow, 9-12 June 1986, Vol. 1, paper 2.3, N.E.L. 4 Mark, P. A., Sproston, J. L. and Johnson, M. W. 'Theoretical and experimental studies of turbine meters in twophase flows', In Int. Conf. on Basic Principles and Industrial Applications of Multiphase Flow, London, 24-25 April 1990, IBC Technical Services Ltd