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Mass Flowrate Measurement of Wet Steam Using Combined V-cone and Vortex Flowmeters Jinxia Li, Chao Wang*, Hongbing Ding, Hongjun Sun Tianjin Key Laboratory of Process Measurement & Control School of Electrical and Information Engineering Tianjin University, Tianjin 300072, China
[email protected] Abstract—The accurate measurement of wet steam has great significance for energy conservation and sufficient utilization. However, subject to the complex flow characteristics of vapor steam and discrete droplets, there are many problems in wet steam metrology. A dual-parameter model combining V-cone and vortex flowmeters was proposed to calculate mass flowrate of wet steam. The vapor mass flowrate is obtained by vortex meter coefficient and vapor density; its over-reading is obtained by the measured V-cone two-phase differential pressure and vapor density. The ratio of these two results was defined as overreading factor. The correlation between over-reading factor and Lockhart Martinelli parameter is established by calibration experiments to get the dryness and the mass flowrate of wet steam. The proposed wet steam meter predicts the wet steam mass flowrate within the accuracy of ±6% from 95% tested samples, which indicates the efficiency of the proposed approach was validated. Keywords—Wet steam two-phase flow; V-cone and Vortex street; Dual-parameter method; Mass flowrate; Dryness
I. INTRODUCTION As an important clean energy, steam is widely used in industrial process. Due to energy loss during the long-distant transport, superheated steam gradually condenses and then becomes wet steam [1]. The accurate measurement of wet steam has great significance for energy conservation and sufficient utilization [2]. However, due to the complicated flow characteristics of vapor steam and discrete droplets, the measurement accuracy of wet steam needs to be further improved [3]. At present, differential pressure (DP) flowmeters, ultrasonic, vortex, turbine and Coriolis flowmeters are widely applied in the steam measurement [4]. However, there are still many problems in current research , such as over-reading of differential pressure [5], under-reading of vortex mass flowrate [6], affected by temperature and flow pattern [7]. A new approach combining multi-flowmeters provides the probability for accurately measuring wet steam [8]-[10], among which dual-DP combination were most studied, yet the simultaneous equations can’t be solved due to the similar DP correlations. The combination of V-cone and vortex flowmeters not only integrates the advantages of two kinds of flowmeter, but also avoids the problem of unsolvable simultaneous equations, has been applied to different flow measurements [11]-[12]. For example, Sun et al. [13] measured the mass flow measurement of gas–liquid bubble The research work is supported by National Science Foundation of China under Grant 61627803, 51506148 and 61673291, Natural Science Foundation of Tianjin under Grant 16JCQNJC03700 and 15JCYBJC19200
978-1-5090-3596-0/17/$31.00 ©2017 IEEE
flow using a Venturi tube and a vortex flowmeter based on the aqual mass flowrate of mixed phase measured by Venturi and vortex flowmeter, Hua and Geng [14] designed a wet gas meter based on the combination of vortex precession frequency and the DP signal of swirl meter, which was emphasized on the more accurate mass flowrate measurement of gas phase. In addition, with the advantages of low cost, stable signal, and wide measurement range , V-cone also has a strong anti– disturbance of upstream and self-cleaning ability, and is widely applied in steam measurement. In this study, the dualparameter model was proposed combing V-cone and vortex flowmeters to accurately calculate steam mass flowrate. The calibrated vortex meter coefficient and the Over-Reading model of V-cone in wet steam flow were discussed in detail. II. MEASURING THEORY A. Mass flowrate of V-cone flowmeter
Fig. 1 Structure of the V-cone flowmeter
The structure and size of V-cone flowmeter are shown in Fig. 1. When the fluid goes through the cone, the gradually converging cross-area makes the fluid accelerate and subsequently a pressure drop appears. The mass flowrate of single phase flow is calculated by this DP signal, as follows, Wm =
ε CD A 1− β 4
2 ρΔP = K1 ρΔP
(1)
where Wm is the mass flowrate (kg/s), ε is the expansibility factor (İ = 1, for incompressible fluid, İ < 1, for compressible fluid), CD is the discharge coefficient, A is the minimum passthrough cross-section area, β is the the equivalent diameter ratio, ρ is the fluid density, οP is the pressure drop (Pa), and Κ1 is the meter coefficient. There are three key parameters affecting the meter’s performance: the equivalent diameter ratio (β), the front cone angle (α1) and the back cone angle (α2) (see Fig. 1). In
consideration of the value and stability of CD, β is set to be 0.80 [15]. The cone with front angle α1 = 45° and back angle of α2 = 120° are select for their widest measuring range and optimized influence on CD [15]. B. Volume flowrate of vortex flowmeter
Fig. 2 The diagram of vortex-street and size of the bluff body
The diagram of vortex street is shown in Fig. 2. When fluid flows around the bluff body, flow separation occurs because of viscous dissipation and wall effect, and vortex forms constantly due to the backflow of the fluid within the boundary layer separation surface F-Q. Under right condition, vortex sheds on both sides of the bluff body alternatively in frequency f, forming Karman vortex-street. The volume flowrate is a linear function of frequency f 4 Sr Qv = f / K 2 , K 2 = π D 2 md
(2)
where K2 is the meter coefficient, Sr is the Strouhal number, d is the width of bluff body, D is the pipe diameter, m is the ratio of circulation area and pipe section area. For single-phase vortex street, K2 is a constant over a wide range of Re number. For wet steam with lower liquid fraction, the effects of dryness on vortex flowmeter is very small and meter coefficient K2 is approximately a constant [16]. However, K2 may change under different pressure and temperature conditions, and need to be calibrated in actual wet steam case. III. MEASUREMENT MODEL BASED ON V-CONE AND VORTEX FLOWMETERS
A. Model description The combination of V-cone and vortex flowmeters is shown in Fig. 3. Along the flow direction, from left to right are: platinum thermal resistance, vortex flowmeter, pressure gauge and V-cone. The inner diameter of the pipeline D is 50 mm, and the distance between vortex flowmeter and V-cone is 257 mm. The temperature T, vortex frequency f, pressure P and differential pressure ΔP all input terminal for data processing.
Fig. 3 Combination of V-cone and vortex flowmeters
The flow chart of information for the wet steam mass flowrate estimation is shown in Fig. 4. The vapor phase mass flowrate QmG is calculated by the calibrated vortex meter coefficient K2 and vapor density, the over-reading of vapor phase mass flowrate QmTP is obtained by the measured differential pressure and vapor density, and the ratio of these two mass flowrates is Over-Reading factor OR. The correlation between OR and the Lockhart Martinelli parameter XLM is established by calibration experiments, which could be used to get the intermediate variable dryness x, and further the mass flowrate of the wet steam Qm.
ΔP Qmv = f / K 2
ρG , ρL
OR = f ( X LM )
QmG = Qmv ⋅ ρG WmTP = K1 ρ G ΔpTP
Qm = WmTP = OR QmG
QmG x
Fig. 4 Flow chart of information for the wet steam mass flowrate estimation
Based on above model, the key problem is to study the V-cone pressure drop model, and establish the correlation between Over-Reading factor OR and the Lockhart Martinelli parameter XLM by calibration experiments. B. Steam Over-Reading model The Homogeneous model and Separated flow model are the basic models in two-phase flow measurement with DP meters, and other DP correlations available are developed from them, such as Murdock correlation [19], Chisholm correlation [20], Smith and Leang correlation [21] and Lin correlation [22] and so on. In order to get the actual pressure drop of V-cone in wet steam two-phase flow, the Over-Reading correlation was derived based on the Separated flow model, which assumes that the two-phase flow is treated separately as two single incompressible fluids flowing alone without phase transformation and expansion with their own flow parameters and properties but with identical discharge coefficients and differential pressures to each other [23]. The mass flowrate equations of the vapor phase and liquid phase respectively when it passes through the V-cone individually are QG = QL =
ε1CA 1− β 4
ε 2CA 1− β 4
2ΔpG 0 ρ G
(3) 2ΔpL0 ρ L
where subscript ‘G’ and ‘L’ denotes vapor phase and liquid phase respectively. The mass flowrate equations of the vapor phase and the liquid phase when two-phase flow passes the DP meter are:
QG = QL =
ε1CAG 1− β 4
ε 2CAL 1− β 4
2ΔpTP ρ G 2ΔpTP ρ L
(4)
A = AG + AL
The pressure drop correction of the Separated flow model deduced from Eq. (3) and Eq. (4) is Fig. 5 The diagram of the wet steam field device and pipeline.
ΔpTP ΔpL0 =1+ ΔpG ΔpG 0
(5)
The pressure drop correction could be simplified by the Lockhart Martinelli parameter XLM, i.e OR = 1 + X LM ,
X LM =
mL mG
ρG ρL
(6)
where OR is the Over-Reading factor and refer to the mass flowrate of the wet steam two-phase flow through V-cone being larger than the mass flowrate of vapor-phase with the same inlet value in the two-phase flow. The results by using Separated flow model is usually relatively different from the actual values due to the complexity of vapor steam. Many researchers obtained the modified DP corrections through a series of experiments, such as Murdock correction [19] OR = 1 + 1.26 X LM (7) Compared with Eq. (6), Eq. (7) has another more coefficient 1.26 and is in good agreement with the experimental data. Based on separated flow model, Lin [22] put forward an Over-Reading correlation, as follows, by using the similarity theory OR = 1 + θ ⋅ X LM (8) where correction factor θ depends on density ratio, i.e. θ = f ( ρG / ρ L ) , whose value should be determined by experiments. IV. STEAM CALIBRATION FOR MEASUREMENT MODEL A. Experiment rig The diagram of the wet steam field device is shown in Fig. 5. Water was heated to be superheated steam in boiler, after filtered and pressure stabilizing, superheated steam flowed into the desuperheater and buffer tank. The flowrate of steam was regulated by valve to reach stable pressure and flowrate. The inner diameter of the pipeline was 50 mm, the superheated steam gradually condensed and then became wet steam during the long-distant transport. The tested V-cone and vortex flowmeter was installed on full development downstream, where both thermal equilibrium and force balance was reached. The water mass flow in the boiler was measured by electronic weighing, and the cumulative mass flow of wet steam was equal to the mass reduction of water in boiler, then the instantaneous mass flowrate of wet steam could be obtained.
Wet steam temperature was measured by Pt100 platinum resistance with the maximum error 0.2 Ԩǡ the range of pressure gauge was 0-10 MPa with the measurement accuracy of 1.6%, the range of differential pressure transmitter was 0-20 KPa and the measuring accuracy is 2%. The range of field dryness x=0.54-0.94, absolute pressure p=4.31-8.62 MPa, temperature T=519-561 K. B. The formula of wet steam mass flowrate The volume flowrate could be obtained by the calibrated vortex meter coefficient K2 and measured frequency f. The volume flowrate of vapor phase can be considered to be equal to that of wet steam in view of the very small liquid fraction. The vapor density is calculated by IAPWS-IF97 [24], and the mass flowrate of vapor phase QmG =
f ⋅ ρG K2
(9)
The Over-Reading mass flowrate of vapor phase measured by V-cone can be calculated by WmTP = K1 ρG ΔpTP (10) The location of vortex flowmeter is close with V-cone, consequently, the actual mass flowrate of vapor phase WmG equals that measured by vortex flowmeter QmG, the OverReading factor is calculated by OR =
WmTP WmTP K1K 2 = = WmG QmG f
ΔpTP
ρG
(11)
The Over-Reading correlation is calibrated using 180 sets of experimental data, and the trend chart of OR with the Lockhart Martinelli parameter XLM is shown in Fig. 6. The Over-Reading factor OR increases linearly with XLM, and the growth rate of OR is related with density ratio, which is consistent with the aforementioned Lin correlation [22]. Fit the test data in accordance with the following form OR = 1 + (a − b ⋅
ρG ) X LM ρL
(12)
where coefficient a=3.3, b=22.5. The experimental fitting error (Fig. 7) is within ±2% , indicating a good fitting effect.
12
1.40
10
1.30
Measured Qm (kg/h)
Over-Reading factor
1.35
1.25 1.20 ρG / ρL = 0.03
1.15
ρG / ρL= 0.04
1.10
ρG / ρL= 0.05
1.05 1.00 0.00
0.03
0.06
0.09 XLM
0.12
-10%
6 4
0.15
2
0.18
2
4
6
8
Actual Qm (kg/h)
10
12
Fig. 8 Experimental error of wet steam mass flowrate and the relation between the measured and inlet actual value
5 4
9
3
6
2 Relative error of Qm (%)
Relative error of Over-Reading (%)
8
ρG / ρL = 0.055
Fig. 6 Trend chart of Over-Reading factor OR with XLM
1 0 -1 -2 -3 -4 -5 0.00
0.03
0.06
0.09
0.12
0.15
0.18
The dryness correlation could be deduced by Eq. (12), as follows ρG / ρ L ρG / ρL (13) = º X LM + ρ G / ρ L ª K1K 2 ΔpTP ρG − 1» / ( a − b ⋅ ) + ρ G / ρ L « ρG ρL »¼ ¬« f
Based on Eq. (9) and Eq. (12), the mass flowrate of wet steam are deduced as follows ΔpTP
ρG
º ρ − 1» / ( a − b ⋅ G ) + ρG / ρ L ρL »¼ ρG / ρ L
(14)
V. RESULTS ANALYSIS AND DISCUSSION The experimental errors of dual-parameter model are discussed with another 500 sets of data besides the calibration experiments, and the relative experimental error is defined by the following equation Vmeasured − Vactual × 100% (15) Vactual The comparison of measured wet steam mass flowrate by Eq. (14) and actual inlet mass flowrate is shown in Fig. 8, and the relative error is shown in Fig. 9. The relative error is within ±6% from 95% tested samples, and the maximum error is10% . ER =
0 -3 -6 -9
-15
Fig. 7 Fitting error of Over-Reading factor
ª K1K 2 « QmG f ⋅ ρG «¬ f Qm = = ⋅ x K2
3
-12
XLM
x=
+10%
2
4
6 8 Actual Qm (kg/h)
10
12
Fig. 9 Relative error of the wet steam mass flowrate with the inlet actual wet steam mass flowrate
There are many factors that would influence the accuracy of the wet steam mass flowrate measurement, and it is an important issue to find the major factor contributing to error distributions, then further optimize the predication model. The Lockhart Martinelli parameter, field pressure, vortex frequency and V-cone differential pressure are the most influential factors to wet steam mass flowrate, and the relative error with these variable is shown in Fig. 10. With the increase of XLM, the relative error increases and shifts negatively, which indicates that the model prediction is some lower under high liquid holdup condition, and the increasing negative error might attributed to the constant value assumption of vortex meter coefficient, which may affected by the dryness of wet steam. The relative error tends to increase with field pressure, which manifests that the impact of high pressure should be considered and appropriate modification need to be conducted to further improve the prediction accuracy. The other measured variable, such as V-cone differential pressure and vortex frequency, their change doesn’t cause obvious trend in relative error, ruling out their direct influence on wet steam mass flowrate accuracy. In addition, the more accurate and over-reading model can be considered to further improve the prediction accuracy.
flowrate of wet steam. The vortex meter coefficient was calibrated and the Over-Reading correlation with the Lockhart Martinelli parameter was established by field experimental data. The intermediate variable dryness could be obtained by the calibrated OR- XLM correlation, then the mass flowrate of the wet steam could be calculated.
(a) 9
Relative error of Qm (%)
6 3 0 -3 -6 -9
-12 -15
0.03
0.06
0.09
0.12 XLM
0.15
0.18
0.21
(b) 9 Relative error of Qm (%)
6
The proposed wet steam meter predicts the wet steam flowrate within ±6% from 95% tested samples, and the maximum error is10% , which indicates that it is effective to measure the mass flowrate of wet steam with the proposed combination method. In addition, from the relative error distributions of wet steam mass flowrate, the predication accuracy is susceptible to high liquid holdup and high field pressure, and could be targeted to be modified to further improve the prediction accuracy.
3
ACKNOWLEDGEMENT This work is supported by National Natural Science Foundation of China under Grant 61627803, 51506148 and 61673291, Natural Science Foundation of Tianjin under Grant 16JCQNJC03700 and 15JCYBJC19200, Research Fund of Tianjin Key Laboratory of Process Measurement and Control under Grant TKLPMC-201611.
0 -3 -6 -9
-12 -15 4.0
4.5
5.0
5.5
6.0 6.5 P (MPa)
7.0
7.5
8.0
REFERENCES
(c) 9
[1]
Relative error of Qm (%)
6
[2]
3 0
[3]
-3 -6
[4]
-9
-12
[5]
-15
50
100
150
f (Hz)
200
250
300
(d) 9
[6]
Relative error of Qm (%)
6
[7]
3 0
[8]
-3
[9]
-6 -9
[10]
-12 -15
0
10
20
30
40
50
60
70
80
ΔP (kPa)
Fig. 10 Distributions of the relative error of the wet steam mass flowrate (a) error versus the Lockhart Martinelli parameter (b) error versus field pressure (c) error versus vortex frequency (d) error versus V-cone differential pressure
VI. CONCLUSIONS Dual-parameter model based on the combination of Vcone and vortex flowmeter was proposed to measure the mass
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