A Simplified Numerical Approach to Examine the Sensitivity of Two-Electrode Capacitance Sensor Orientation to Capture Different Gas–Liquid Flow Patterns in a Small Circular Pipe
Abstract
:1. Introduction
1.1. Sensors in Multiphase Flow
1.2. Two-Electrode Capacitance Sensors in Gas–Liquid Multiphase Flow
2. Experimental Apparatus and Methodology
3. Numerical Approach
- (a)
- For all the simulated flow patterns, the flow was advancing by 2 mm step until the entire structure of the flow pattern passed the capacitance sensor;
- (b)
- The period of time for the simulation was then taken as identical to the time elapsing in the real experiment while the same number of iterations of the flow pattern crossed the capacitance sensor;
- (c)
- In the small bubble flow pattern, the average sizes of the largest small bubbles and the smallest small bubbles were taken from the high-speed camera images;
- (d)
- The plug and elongated bubble flow patterns have the same hydrodynamic mechanism, however, the sizes of the bubbles are different;
- (e)
- The slug and slug–churn flow patterns have the same hydrodynamic mechanism, however, the slug–churn is frothier (this was implemented by having changing permittivity);
- (f)
- For the annular flow pattern, the pipe wall was assumed to be wetted by a symmetrical liquid film of a thickness of 1 mm over the entire length of the model, except for the section before the capacitance sensor screen, where the thickness of the film was 3 mm, as the simulation was run, this thicker film advanced through the capacitance sensor in 2 mm steps until it filled the entire length of the model. The model assumed that the thickness of the liquid would be symmetric around the pipe;
- (g)
- Regardless of the inclination, the numerical model treated each flow pattern similarly for all inclinations. In other words, for example, the simulated small-bubbles/slug flow pattern is the same in structure for all inclination. The only two differences are (1) the combination of gas–liquid superficial velocities at which these flow patterns were induced due to the effect of gravity and inclination, and (2) some flow patterns did not form or develop in a certain inclination (i.e., the plug flow pattern at a horizontal 0°, and the stratified wavy at all upward inclined angles [28,32]).
4. Results and Discussion
4.1. Time Dependent Analysis
4.1.1. Small Bubble Flow Pattern
4.1.2. Plug and Elongated Flow Patterns
4.1.3. Slug and Slug–Churn Flow Patterns
4.1.4. Stratified Wavy and Annular Flow Patterns
4.2. Optimizing Electrodes Orientation
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Latin Symbols | |
C | Capacitance, pF |
CG | Gas capacitance, pF |
CL | Liquid capacitance, pF |
CWall | Wall capacitance, pF |
D | Electric displacement (vector), C/m2 |
din | Inner pipe diameter, mm |
dout | Outer pipe diameter, mm |
da | Infinitesimal area on closed surface, m |
E | Electrical field, V/m |
n | A unit vector perpendicular to da, - |
Q | Surface charge, C |
S | Closed surface |
uGS | Superficial gas velocity, m/s |
uLS | Superficial liquid velocity, m/s |
ut | Translational velocity, m/s |
V(x,y,z) | Electric potential distribution, V |
x(n) | Discrete time signal, units depend on application |
Greek Symbols | |
Permittivity of free space, F/m | |
Permittivity distribution, - | |
External charge density C/m3 | |
Other Symbols | |
Gradient operator | |
Divergence operator |
Appendix A
Numerical Model Spikes Rationale
References
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Type of Sensor | Principle of Work | Usefulness |
---|---|---|
High-speed camera images ([10]) |
|
|
Photochromic dye activation ([11,12]) |
|
|
Particles image velocimetry (PIV) ([13]) |
|
|
Acoustic techniques ([14]) |
|
|
Optical fiber probes ([15]) |
|
|
Two hot film anemometers ([16]) |
|
|
Conductivity and conductance probes ([17,18,19,20]) |
|
|
Tomographic methods ([21,22,23,24,25,26]) |
|
|
Static/differential pressure ports ([27]) |
|
|
Component | Dimension | Specification |
---|---|---|
Test section | l = 4 m, din = 20 mm, and dout = 24 mm | Transparent acrylic pipe |
Air compressor system | Brass pipe, l = 2.50 m, and din = 9.0 mm | - |
A metering system to the supply air | - |
|
Turbine flowmeter | - | FTB790-Omega, accuracy of ±0.2% |
Gas–liquid mixer | l = 280 mm, internal pipe din = 20 mm | 100 holes, 1 mm in diameter, dispersed 10 mm apart in the axial direction and 5 mm away from each other on the circumference |
Swing table | - | Inclination range from 0° to 30° |
High-speed camera images | 2 min, shutter speed = 1/10,000 s, frame rate = 500/s | Installed at 3.4 m after the inlet of the test section |
Tank | V1 = of 0.288 m3 (main) V2 = of 0.166 m3 (return) | - |
Submersible pump | - | 70 L/min |
Capacitance sensor (two electrodes [32]) | din = 24 mm, dout = 54 mm, l = 54 mm, gap between electrodes = 6 mm, insulation l = 50 mm, and brass screen thickness = 2 mm | C1 at 3 m and C2 at 3.25 m from the inlet |
Flow Pattern Type | Inclination | |||||
---|---|---|---|---|---|---|
Horizontal 0° | Upward 15° | Upward 30° | ||||
Range of Gas–Liquid Phases Superficial Velocities (m/s) | ||||||
Gas Phase | Liquid Phase | Gas Phase | Liquid Phase | Gas Phase | Liquid Phase | |
Small bubbles | 0.040–0.050 | 0.70–1.1 | 0.035–0.048 | 0.318–1.1 | 0.025–0.065 | 0.425–1.1 |
Plug * | N/A | N/A | 0.127–0.50 | 0.53–1.1 | 0.051–0.314 | 0.21–1.1 |
Elongated bubbles | 0.15–0.74 | 0.42–1.1 | 0.25–0.75 | 0.32–1.1 | 0.055–0.576 | 0.11–1.1 |
Slug | 0.37–2.29 | 0.316–1.1 | 0.70–2.18 | 0.12–1.1 | 0.47–2.86 | 0.11–0.95 |
Slug–churn | 2.11–3.74 | 0.425–1.1 | 2.90–4.40 | 0.11–1.1 | 2–4.29 | 0.10–1.1 |
Annular | 4.48–5 | 0.31–1.1 | 4.75-5 | 0.106–1.1 | 4–5 | 0.11–1.1 |
Stratified wavy * | 1.24–3 | 0.1–0.32 | N/A | N/A | N/A | N/A |
Type of Flow Pattern | Arrangement | Cross-Sectional View | Explanation | Number of Times Passed the Capacitance Sensor | 3D Demonstration of the Defined Model Geometry |
---|---|---|---|---|---|
Small bubble | | | 2 different sizes of small spherical bubble | 100 in 10 s | |
Plug | | | Cylindrical bubble | 9 times, 9 cap bubbles in 3 s | |
Elongated bubble | | | Large cylindrical bubble | 15 times, 15 elongated bubbles in 4 s | |
Slug | | | Start with a concave-shaped liquid at bottom, and later a pipe filled with liquid phase | 8 times, 8 slugs in 5 s | |
Slug–churn | | | Pipe divided into 8 different permittivity sections | 8 times, 8 slug–churns in 5 s | |
Annular | | | Symmetrical liquid film of thickness 1 mm, then increased by 2 mm | 15 times, 15 spikes in 5 s | |
Stratified | | | Starts with liquid up to the midline of the pipe, then a square wave of liquid crosses the sensor | 8 times, 8 waves in 5 s | |
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Al-Alweet, F.M.; Jaworski, A.J.; Alghamdi, Y.A.; Almutairi, Z.; Kołłątaj, J. A Simplified Numerical Approach to Examine the Sensitivity of Two-Electrode Capacitance Sensor Orientation to Capture Different Gas–Liquid Flow Patterns in a Small Circular Pipe. Sensors 2020, 20, 4971. https://doi.org/10.3390/s20174971
Al-Alweet FM, Jaworski AJ, Alghamdi YA, Almutairi Z, Kołłątaj J. A Simplified Numerical Approach to Examine the Sensitivity of Two-Electrode Capacitance Sensor Orientation to Capture Different Gas–Liquid Flow Patterns in a Small Circular Pipe. Sensors. 2020; 20(17):4971. https://doi.org/10.3390/s20174971
Chicago/Turabian StyleAl-Alweet, Fayez M., Artur J. Jaworski, Yusif A. Alghamdi, Zeyad Almutairi, and Jerzy Kołłątaj. 2020. "A Simplified Numerical Approach to Examine the Sensitivity of Two-Electrode Capacitance Sensor Orientation to Capture Different Gas–Liquid Flow Patterns in a Small Circular Pipe" Sensors 20, no. 17: 4971. https://doi.org/10.3390/s20174971
APA StyleAl-Alweet, F. M., Jaworski, A. J., Alghamdi, Y. A., Almutairi, Z., & Kołłątaj, J. (2020). A Simplified Numerical Approach to Examine the Sensitivity of Two-Electrode Capacitance Sensor Orientation to Capture Different Gas–Liquid Flow Patterns in a Small Circular Pipe. Sensors, 20(17), 4971. https://doi.org/10.3390/s20174971