# Measurement of local two-phase flow parameters of nanofluids using conductivity double-sensor probe

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## Abstract

A two-phase flow experiment using air and water-based γ-Al_{2}O_{3} nanofluid was conducted to observe the basic hydraulic phenomenon of nanofluids. The local two-phase flow parameters were measured with a conductivity double-sensor two-phase void meter. The void fraction, interfacial velocity, interfacial area concentration, and mean bubble diameter were evaluated, and all of those results using the nanofluid were compared with the corresponding results for pure water. The void fraction distribution was flattened in the nanofluid case more than it was in the pure water case. The higher interfacial area concentration resulted in a smaller mean bubble diameter in the case of the nanofluid. This was the first attempt to measure the local two-phase flow parameters of nanofluids using a conductivity double-sensor two-phase void meter. Throughout this experimental study, the differences in the internal two-phase flow structure of the nanofluid were identified. In addition, the heat transfer enhancement of the nanofluid can be resulted from the increase of the interfacial area concentration which means the available area of the heat and mass transfer.

### Keywords

Test Section Void Fraction Lift Force Heat Transfer Enhancement Interfacial Velocity## Introduction

The conventional method of increasing the cooling rate is to use extended heat transfer surfaces for exchanging heat with a heat transfer fluid. However, because this approach requires an undesirable increase in the size of the system, there is a need to develop advanced cooling techniques and innovative heat transfer performances than those presently available. Over the last several decades, engineers have attempted to develop fluids which offer better cooling performances for a variety of thermal systems compared to conventional heat transfer fluids. This motivation inspired Choi [1] to pioneer the development of nanofluids. A nanofluid is a new type of fluid that consists of uniformly dispersed and suspended nanometer-sized particles or fibers in fluids with unprecedented thermal characteristics.

Numerous research groups from around the world have published a large number of experimental and theoretical studies on nanofluids. A certain group argued that nanofluids substantially enhance the heat transfer rate compared to the pure water, while the others found that the inclusion of nanoparticles degraded the boiling performance with increasing the particle concentration. Despite these conflicting research results, the impact of nanofluid technology is expected to be great considering that the heat transfer performance of heat exchangers is vital in numerous industries. In addition, due to the small size of nanoparticles and low volume fraction, problems such as sedimentation, clogging, and abrasion become insignificant with the reduction in required pumping power.

While a considerable body of research exists regarding the heat transfer characteristics of nanofluids, the basic hydraulic phenomenon of a nanofluid, especially in the two-phase flow region, has not been investigated as much. Moreover, there was no attempt to identify the internal structure of the two-phase flow of nanofluids. Hence, in this study, a two-phase flow experiment using an air-nanofluid was conducted. To observe the basic hydraulic phenomenon of nanofluids, the local two-phase flow parameters such as void fraction distribution and interfacial area concentration were measured using a conductivity double-sensor two-phase void meter in a vertically upward air-water two-phase flow. The results obtained from the nanofluids were compared with the results obtained from pure water.

## Experimental apparatus

In this experiment, a double-sensor two-phase void meter was used as the phase identifier for the two-phase mixture. The conductivity double-sensor two-phase void meter was first proposed by Neal and Bankoff [2]. The double-sensor electrodes consist of two exposed tips, a front sensor and a rear sensor, besides an electrically insulated metal wire and work independently. By considering the fundamental difference in the conductivity between water and air, the circuit is closed when the sensor is in the liquid and is opened when the sensor is in contact with air. The voltage drop across the sensor fluctuates between two reference voltages when the circuit is opened and closed. The information recorded from each signal includes the number of bubbles that strike the sensor, the time that the sensor is exposed to the gas phase, the relative time between the bubble striking the front and rear sensor, and the total sampling time. This information is used to calculate the local two-phase flow parameters: namely, the void fraction, the bubble diameter, the interfacial velocity, and the interfacial area concentration.

Test cases for the local two-phase flow measurement

Case number | Liquid flow rate (m | Air flow rate (m | Flow regime | Case number | Liquid flow rate (m | Air flow rate (m | Flow regime |
---|---|---|---|---|---|---|---|

1 | 0.00026 | 0.000033 | Bubbly | 8 | 0.0006 | 0.000083 | Bubbly |

2 | 0.00039 | 0.000513 | Slug | 9 | 0.0005 | 0.00005 | Bubbly |

3 | 0.00039 | 0.000890 | Slug | 10 | 0.0005 | 0.000033 | Bubbly |

4 | 0.00055 | 0.000513 | Slug | 11 | 0.00018 | 0.000513 | Slug |

5 | 0.00055 | 0.000890 | Slug | 12 | 0.00018 | 0.000033 | Bubbly |

6 | 0.00056 | 0.000513 | Slug | 13 | 0.00018 | 0.000333 | Slug |

7 | 0.00056 | 0.000033 | Bubbly | - |

_{2}O

_{3}nanoparticle powder manufactured by Nanostructured & Amorphous Materials Inc. (Houston, TX, USA) was used. The average particle size of the powder was 25 nm at 99.97% purity based on the information provided by the manufacturer. After the mixing of the γ-Al

_{2}O

_{3}powder with distilled water, it was placed in an ultrasonic bath for an hour for particle dispersion. The nanofluid was then placed in a room temperature atmosphere for 24 h to form an electrical double layer, which makes the nanofluid more stable. This synthesized nanofluid was placed in the ultrasonic bath again for 1 h immediately before the experiment. For a stability check, the zeta potentials were measured before and after the experiments for several concentrations of the γ-Al

_{2}O

_{3}nanofluid. The average values are shown in Table 2; the most stable case of 0.1% was the target concentration for the analysis and discussion.

Zeta potentials and particle sizes of the synthesized nanofluids

Volume percent of γ-Al | Zeta potential (mV) | Particle size (nm) | ||
---|---|---|---|---|

Before | After | Before | After | |

0.01 | 31.93 | 26.27 | 100.13 | 169.48 |

0.1 | 42.33 | 36.88 | 158.43 | 142.73 |

1 | - | - | 125.15 | 133.15 |

## Data reduction

### Fluid properties

Equation 2 can be applied to volume fractions of less than 5.0 vol.%. In the present study, the volume concentration of nanoparticle used was 0.1%; thus, this equation can be applied to estimate the viscosity of the nanofluid [7].

### Void fraction

*A*and the cross-sectional areas occupied by the gas and liquid phases are

*A*

_{g}and

*A*

_{f}, respectively, then the void fraction is given by

### Interfacial velocity

*s*, and the time difference between the front and rear signal,

*t*

_{F1}-

*t*

_{R1}[3]. The distance between the tips of the front and rear sensor of the conductivity double-sensor two-phase void meter which was used in this experiment was 1.229 mm. The time-averaged interfacial velocity is determined by Equation 5.

### Interfacial area concentration

The interfacial area describes the available area for the interfacial transfer of the mass, momentum, and energy. The interfacial area concentration is defined as the interfacial area per unit volume of the mixture. Its mathematical formula was proposed by Ishii [8].

Here, Open image in new window and *φ*_{ j }are the interfacial velocity of the *j* th interface and the angle between Open image in new window and the unit normal vector of the *j* th interface, respectively [3].

### Sauter mean diameter

*d*

_{s}, and the volume diameter,

*d*

_{v}. The surface diameter is expressed as

*A*

_{p}and

*V*

_{p}are the surface area and volume of the particle, respectively. The Sauter mean diameter for a given particle can then be expressed as

## Results

In the bubbly flow regime, as shown in Figure 4, the maximum value of the void fraction distribution is approximately 0.18 in the case of the nanofluid; this value is smaller than that of pure water, 0.225, at the center of the test section. The decrease in the rate of occurrence of void fractions in the nanofluid becomes smaller than that of pure water as the sensor approaches the wall. Thus, the overall shape of the void fraction distribution was flattened more in the case of nanofluids than in the case of pure water. The bubble velocity also decreased in the case of the nanofluid. However, the interfacial area concentration was increased and it was significant as the sensor approached to the wall. And the mean bubble diameter, as determined from the void fraction and interfacial area concentration, was decreased.

In the slug flow regime, as shown in Figure 5, a wider and flatter void fraction distribution compared to that of the pure water was also shown in the nanofluid results. The bubble velocity in the nanofluid case shows a value that is higher than that of the pure water case near the center of the test section. The interfacial area concentration of the nanofluid case also shows a higher value compared to the pure water. Especially in the case of the nanofluid, the interfacial area concentration increased significantly in the vicinity of the wall. This can be concluded that the boundary of air slug and liquid film is located at this point, and the shorter lengths of air slugs pass the void meter in the nanofluid case than in the pure water case. In the mean bubble diameter result, the smaller air slug size in the nanofluid case than that in the pure water case was evaluated as it was reflected in the interfacial area concentration result.

## Discussion

In this experiment, the void fractions were flattened with smaller bubbles in the case of nanofluids. The flattening of the void fraction distribution in the nanofluid can be explained by the forces that act between the two phases. The types of forces that act between the two phases include drag force, lift force, wall lubrication force, and turbulence dispersion force. The main determinant of the transverse motion of the bubbles is the interaction between the drag force and the lift force.

*U*

_{T}, is outlined in the ANSYS CFX Solver Theory Guide (ANSYS, Inc., Canonsburg, PA, USA) [9]. To evaluate the drag coefficient using the Grace model, mean bubble diameter is the starting point. As shown in Figure 4, mean bubble diameter ranges from 0 to 0.0079 m for the pure water and from 0 to 0.0034 m for the nanofluid. Within this range of bubble sizes, the drag coefficients are calculated with the fluid properties of the pure water and the nanofluid; the results are shown in Figure 6. The drag coefficient of the small bubbles is about 13 to 22 in the nanofluid and almost 12 in the pure water. In addition, the drag coefficient of the nanofluid is larger than that of the pure water (about 6%) within the same bubble sizes. Thus, the drag force acting on the rising bubbles in the nanofluid case is larger than in the pure water case.

From these results, it can be concluded that the flattened void fraction in the nanofluid means that the bubbles in the nanofluid smaller than those of pure water were passed in the flow under the force acting in the direction of the wall.

## Conclusion

In this experimental study, a basic hydraulic experiment using a water-based γ-Al_{2}O_{3} nanofluid was conducted. Air and the nanofluid were used as working fluids in a vertically upward acrylic tube. The local two-phase flow parameters such as the void fraction, the interfacial velocity, the interfacial area concentration, and the mean bubble diameter were measured using a conductivity double-sensor two-phase void meter in bubbly and slug flow regimes. The void fraction distribution was flattened in the nanofluid case more than it was in the pure water case. The higher interfacial area concentration resulted in a smaller mean bubble diameter in the case of the nanofluid. In view of the forces acting between the two phases, the difference between the nanofluid and pure water can be attributed to the smaller bubbles that form in the nanofluid.

Throughout this experimental study, the characteristics of the internal two-phase flow structure of the nanofluid were specified. In addition, the heat transfer enhancement of nanofluid can be resulted from the increase of the interfacial area concentration which refers to the available area of the mass, momentum, and energy transfer.

### Nomenclature

A cross-sectional area (m^{2})

*a*_{i} interfacial area concentration (1/m)

*C*_{D} drag coefficient

*D* inner diameter of the test section (m)

*d* diameter of a bubble (m)

*g* gravitational acceleration (m/s^{2})

*j* superficial velocity (m/s)

*L* test section length (m)

*N*_{t} total number of bubbles that strike the sensor

Δ*s* distance between the tips of the front and rear sensor (m)

*t*_{F1} time that a bubble starts to hit the front sensor (s)

*t*_{F2} time that a bubble departs from the front sensor (s)

*t*_{R1} time that a bubble start to hit the rear sensor (s)

*Z* height of the test section (m)

*Α* void fraction

*ε* energy dissipation rate per unit mass

*μ* viscosity (N.s/m^{2})

*ν* kinematic viscosity (m^{2}/s)

*ρ* density (kg/m^{3})

*σ* surface tension (N/m)

*φ* volume fraction of nanoparticle

*Ω* total sampling time (s)

### Subscripts

f liquid phase

g gas phase

nf nanofluid

pw pure water

p nanoparticle

## Notes

## Supplementary material

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