Measurement of void fraction in a hollow rectangular tube using capacitance sensors

N.T. Nguyen, T.A. SheddDepartment of Engineering Physics, University of Wisconsin, Madison

Introduction

Voi d fraction is the key physical value for predicting behaviors of two-phase flow including pressure drops, flow regimes, boiling andcondensing het transfer, and wave dynamics. There have been severalmethods for measuring void fraction in a two-phase flow system. Theseinclude quick closing valves, radiation traversing techniques such asgamma-ray/ x-ray absorption and neutron scattering, optical probes,electrical process tomography method, conductance sensors andcapacitance sensors. Each of these methods has its own advantages anddrawbacks. However capacitance sensors are most desirable becausethey are independent to the conductivity of the fluid and can non-intrusively measure volumetric time-averaged void fraction.

Purpose

1. Developing a robust and low cost capacitance void fractionsensor that is capable of accurately and precisely measuring thevolumetric void fraction in a hollow rectangular tube.

2. Conducting a calibration experiment to explore the effect ofcapacitance on the two-phase flow, and using this sensor toacquire void fraction data.

3. Testing and comparing the new data set to available data and voidfraction models in the literature.

Sensor Design

The sensor consists of four rectangular acrylic pieces jointed tightly togetherby using acrylic solvent cement to construct a hollow rectangular pipe withcross-section of 36 mm width and 14 mm height and eighteen electrodes usedto measure capacitance.

E-Field Simulation and Optimization

The principle of the capacitance method is based on the change in thedielectric constant of two-phase as the void fraction changes. There aretwo major factors decides the performance of this sensor, which are thegeometry of the sensor and the dielectric between the electrodes.The sensor can be approximated as a system of four parallel platecapacitors placed in series. Thus, the total capacitance is given,

Principles of Capacitance Sensors

Kε0 is the permittivity of the dielectric, A is the area of each electrode, and d is the distance between electrodes. The area of each electrode is varied to optimize the sensor design using FEHT,

2D finite element electromagnetic field simulation software.The sensor was constructed by the author, and machining was done at theUniversity of Wisconsin Student Machine Shops.

Calibration Methods and Procedure

A schematic diagram of the calibration loop

The sensor with guard electrodes geometry and FEHT simulation

1. Ensure no air bubbles in the tubes connecting thepressure ports to the OMEGA differential pressuretransmitter.

2. The air flow rate is set from 0 to 6 SLM by slowlyturning the rotameter clockwise .

3. Give enough time for the differential pressuretransmitter and rotameter to reach steady stateconditions and run LabVIEW to record data.

Dynamic calibration using pressure drops:

Pressure gradient = Acceleration + Friction + Gravitation

Under bubbly flow with small void fraction condition, pressure dropsdue to friction and acceleration are less compared to that due togravitation and can be neglected. Thus, void fraction can deriveddirectly from the measured pressure drop as

The limitation of this method is from its assumption that the bubblevelocity is approximately same as the liquid velocity. Therefore, thiscalibration cannot be applied to flow regimes with high quality or voidfraction such as annular flow.

Dynamic calibration by observing the water levels:Void fraction is given by the conservation of mass,

H is the original water level and ΔH is an increase in water level.The challenge of this method is how precisely one can measure thedynamic water height under a strong fluctuation at the water surface,especially in presence of Taylor bubbles, that makes the water levelextremely unstable.

Results

Conclusions

y = 1.0025x + 0.0081

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0.000 0.200 0.400 0.600 0.800 1.000 1.200

Void

Fra

ctio

n

Normalized Capacitance

Dynamic calibration curve

1. The sensor read 0.977 pF for all air and 0.484 pF for all liquid. Thus, this design results a total change in capacitance of 0.58 pF.

2. The sensor response is linear over the range of void fraction from 0 to 0.34.

3. Uncertainty of this calibration is from a strong fluctuation at the water surface, especially in presence of Taylor bubbles and differences in velocities between bubbles and water.

4. The void fraction obtained from these two calibration methods are in good agreement.

References

Kannan N. Lyer, “Measurement of void fraction”, Laboratory Manual, Department ofMechanical Engineering, IIT-BombayDevin C. Lowe, “A study on flow regime identification in micro-gravity gas-liquidflow using a capacitance sensor”, Master thesis, University of Saskatchewan, 1997