**6. Validation of interfacial area transport models by experimental data**

In order to confirm the validity of transport equation of interfacial area, comparisons with experimental data were carried out mainly for bubbly flow and churn flow. The transport equation for bubbly flow is given by Eq.(68). This equation includes turbulent diffusion term

Transport of Interfacial Area Concentration in Two-Phase Flow 113

For interfacial area transport due to wake of churn bubble, interfacial area is transported toward the center of pipe. The flux of interfacial area concentration in radial direction Jai, due to churn bubble is related to the terminal velocity of churn bubble. The flux of interfacial area concentration toward the center of pipe is large at near wall and small at the center of pipe. Then, it is simply assumed to be proportional to the distance from pipe center. Finally, the flux of interfacial area concentration in radial direction, Jai due to churn

> ai Cai i R y J K {0.35 gD}a <sup>R</sup>

Then, transport equation of interfacial area concentration based on turbulent transport

1 1 0 35 () () 0

In order to predict radial distribution of interfacial area concentration using Eq.(93) or Eq.(95), radial distributions of void fraction, averaged liquid velocity and turbulent liquid velocity are needed. These distributions were already predicted based on the turbulence

Using transport equation of interfacial area concentration for bubbly flow (Eq.(93) and churn flow (Eq.(95)), the radial distributions of interfacial area concentration are predicted and compared with experimental data. Serizawa et al. (1975, 1992) measured distributions of void fraction, interfacial area concentration, averaged liquid velocity and turbulent liquid velocity for vertical upward air-water two-phase flow in bubbly and churn flow regimes in round tube of 60mm diameter. Void fraction and interfacial area were measured by electrical resistivity probe and averaged liquid velocity and turbulent liquid velocity were measured by anemometer using conical type film probe with quartz coating. Their

For empirical coefficient, Kcai is assumed to be 0.01 based on experimental data. The condition of flow regime transition from bubbly to churn flow is given in terms of area

Figures 11 and 12 show some examples of the comparison between experimental data and prediction of radial distributions of interfacial area concentration in bubbly flow and churn flow. In bubbly flow regime, distributions of interfacial area concentration show wall peak of which magnitude is larger for larger liquid flux whereas distributions interfacial area concentration in churn flow show core peak. The prediction based on the present model

averaged void fraction, based on experimental results which is given by

*<sup>a</sup> . gD R yKd v RyK a R y y Ry <sup>R</sup>* 

model of two-phase flow for bubbly flow and churn flow (Kataoka et al. (2011d)).

(94)

0.2 (96)

(95)

2

*B L Cai i*

bubble is assumed to be given by

model in churn flow is given by

experimental conditions are

Liquid flux, JL: 0.44 - 1.03 m/s

Gas flux, JG: 0 - 0.403 m/s

well reproduces the experimental data.

1

y y *i*

of interfacial area, turbulent diffusion term due to non-isotropic turbulence, sink term due to bubble coalescence and source term due to bubble break up. Each term is separately validated by experimental data.

Kataoka et al. (2011b, 2011c) carried out the validation of turbulent diffusion term of interfacial area, turbulent diffusion term due to non-isotropic turbulence using experimental data of radial distributions in air-water two-phase flow in round pipe under developed region. Under steady state and developed region without phase change, coalescence and break up of bubbles are negligible. Under such assumptions, transport equation of interfacial area concentration based on turbulent transport model, Eq.(68) can be simplified and given by following equation.

$$\mathbf{K}\_{\mathbf{L}}\mathbf{d}\_{\mathrm{B}}\left|\mathbf{v}\_{\mathrm{L}}^{\prime}\right|\frac{1}{\mathbf{R}-\mathbf{y}}\frac{\partial}{\partial\mathbf{y}}\left((\mathbf{R}-\mathbf{y})\frac{\partial\overline{\mathbf{a}\_{\mathrm{i}}}}{\partial\mathbf{y}}\right) + \mathbf{K}\_{\mathrm{2}}\mathbf{a}\mathbf{d}\_{\mathrm{B}}\overline{\mathbf{a}\_{\mathrm{i}}}\frac{1}{\mathbf{R}-\mathbf{y}}\frac{\partial}{\partial\mathbf{y}}\left((\mathbf{R}-\mathbf{y})\frac{\partial\overline{\mathbf{V}\_{\mathrm{L}}}}{\partial\mathbf{y}}\right) = \mathbf{0} \tag{93}$$

Here, R is pipe radius and y is distance from pipe wall. Kataoka's model for turbulent diffusion of interfacial area concentration, (Eqs.(61) , ( 65) and (67)) was used.

Kataoka et al. (2011c) further developed the model of turbulent diffusion term due to nonisotropic turbulence for churn flow. In the churn flow, additional turbulence void transport terms appear due to the wake of large babble as schematically shown in Fig.10.

Fig. 10. Wake in Churn Flow Regime

of interfacial area, turbulent diffusion term due to non-isotropic turbulence, sink term due to bubble coalescence and source term due to bubble break up. Each term is separately

Kataoka et al. (2011b, 2011c) carried out the validation of turbulent diffusion term of interfacial area, turbulent diffusion term due to non-isotropic turbulence using experimental data of radial distributions in air-water two-phase flow in round pipe under developed region. Under steady state and developed region without phase change, coalescence and break up of bubbles are negligible. Under such assumptions, transport equation of interfacial area concentration based on turbulent transport model, Eq.(68) can be simplified

1a 1V Kd v (R y) K d a (R y) 0 R yy y R yy y

Here, R is pipe radius and y is distance from pipe wall. Kataoka's model for turbulent

Kataoka et al. (2011c) further developed the model of turbulent diffusion term due to nonisotropic turbulence for churn flow. In the churn flow, additional turbulence void transport

1B L 2 Bi

diffusion of interfacial area concentration, (Eqs.(61) , ( 65) and (67)) was used.

terms appear due to the wake of large babble as schematically shown in Fig.10.

i L

(93)

validated by experimental data.

and given by following equation.

Fig. 10. Wake in Churn Flow Regime

For interfacial area transport due to wake of churn bubble, interfacial area is transported toward the center of pipe. The flux of interfacial area concentration in radial direction Jai, due to churn bubble is related to the terminal velocity of churn bubble. The flux of interfacial area concentration toward the center of pipe is large at near wall and small at the center of pipe. Then, it is simply assumed to be proportional to the distance from pipe center. Finally, the flux of interfacial area concentration in radial direction, Jai due to churn bubble is assumed to be given by

$$\mathbf{J}\_{\rm ai} = \mathbf{K}\_{\rm Cai} \frac{\mathbf{R} - \mathbf{y}}{\mathbf{R}} \{ 0.35 \sqrt{\mathbf{g} \mathbf{D}} \} \overline{\mathbf{a}\_{\rm i}} \tag{94}$$

Then, transport equation of interfacial area concentration based on turbulent transport model in churn flow is given by

$$\frac{1}{R-y}\frac{\partial}{\partial \mathbf{y}}\bigg( (R-y)K\_1d\_\mathbb{B} \left| v\_l' \right| \frac{\partial \overline{a\_i}}{\partial \mathbf{y}} \bigg) + \frac{1}{R-y}\frac{\partial}{\partial \mathbf{y}} \bigg( (R-y)^2K\_{\text{Cdf}}\frac{0.35\sqrt{\mathbf{g}D}}{R}\overline{a\_i} \bigg) = 0\tag{95}$$

In order to predict radial distribution of interfacial area concentration using Eq.(93) or Eq.(95), radial distributions of void fraction, averaged liquid velocity and turbulent liquid velocity are needed. These distributions were already predicted based on the turbulence model of two-phase flow for bubbly flow and churn flow (Kataoka et al. (2011d)).

Using transport equation of interfacial area concentration for bubbly flow (Eq.(93) and churn flow (Eq.(95)), the radial distributions of interfacial area concentration are predicted and compared with experimental data. Serizawa et al. (1975, 1992) measured distributions of void fraction, interfacial area concentration, averaged liquid velocity and turbulent liquid velocity for vertical upward air-water two-phase flow in bubbly and churn flow regimes in round tube of 60mm diameter. Void fraction and interfacial area were measured by electrical resistivity probe and averaged liquid velocity and turbulent liquid velocity were measured by anemometer using conical type film probe with quartz coating. Their experimental conditions are

Liquid flux, JL: 0.44 - 1.03 m/s

Gas flux, JG: 0 - 0.403 m/s

For empirical coefficient, Kcai is assumed to be 0.01 based on experimental data. The condition of flow regime transition from bubbly to churn flow is given in terms of area averaged void fraction, based on experimental results which is given by

$$
\overline{\alpha} = 0.2 \tag{96}
$$

Figures 11 and 12 show some examples of the comparison between experimental data and prediction of radial distributions of interfacial area concentration in bubbly flow and churn flow. In bubbly flow regime, distributions of interfacial area concentration show wall peak of which magnitude is larger for larger liquid flux whereas distributions interfacial area concentration in churn flow show core peak. The prediction based on the present model well reproduces the experimental data.

Transport of Interfacial Area Concentration in Two-Phase Flow 115

 Experiment Prediction

<sup>0</sup> 0.01 0.02 <sup>0</sup>

D=0.06 m

Distanc from wall y(m)

Atmospheric Pressure

jL=0.737 m/s jG=0.200 m/s

 Experiment Prediction

100

100

200

Interfacial area, ai (1/m)

300

200

Interfacial area, ai (1/m)

300

Fig. 12. Distributions of Interfacial Area Concentration for Churn Flow

**Condition I** 

direction were systematically measured. Experimental conditions are as follows.

Pipe diameter D: 25.4mm, Measuring positions z from inlet: (z/D=12, 65,125),

Hibiki and Ishii (2000a) carried out the validation of their own correlations of sink term due to bubble coalescence (Eq.(72)) and source term due to bubble break up (Eq.(70)) using experimental data. They carried out experiments in vertical upward air water two-phase flow in pipe under atmospheric pressure. In order to validate their interfacial transport model, evolutions of radial distributions of interfacial area concentration in the flow

Distanc from wall y(m)

Atmospheric Pressure

jL=1.03 m/s jG=0.331 m/s

<sup>0</sup> 0.01 0.02 <sup>0</sup>

D=0.06 m

Fig. 11. Distributions of Interfacial Area Concentration for Bubbly Flow

 Experiment Prediction

 Experiment Prediction

 Experiment Prediction

<sup>0</sup> 0.01 0.02 <sup>0</sup>

<sup>0</sup> 0.01 0.02 <sup>0</sup>

<sup>0</sup> 0.01 0.02 <sup>0</sup>

D=0.06 m

Distanc from wall y(m)

D=0.06 m

Atmospheric Pressure

Distanc from wall y(m)

Atmospheric Pressure

jL=1.03 m/s jG=0.132 m/s

jL=0.737 m/s jG=0.135 m/s

Atmospheric Pressure

D=0.06 m

Distanc from wall y(m)

jL=0.442 m/s jG=0.134 m/s

100

100

100

200

Interfacial area, ai (1/m)

300

200

Interfacial area, ai (1/m)

300

200

Interfacial area, ai (1/m)

300

Fig. 11. Distributions of Interfacial Area Concentration for Bubbly Flow

Fig. 12. Distributions of Interfacial Area Concentration for Churn Flow

Hibiki and Ishii (2000a) carried out the validation of their own correlations of sink term due to bubble coalescence (Eq.(72)) and source term due to bubble break up (Eq.(70)) using experimental data. They carried out experiments in vertical upward air water two-phase flow in pipe under atmospheric pressure. In order to validate their interfacial transport model, evolutions of radial distributions of interfacial area concentration in the flow direction were systematically measured. Experimental conditions are as follows.

#### **Condition I**

Pipe diameter D: 25.4mm, Measuring positions z from inlet: (z/D=12, 65,125),

Transport of Interfacial Area Concentration in Two-Phase Flow 117

Fig. 14. Comparison between Experimental data and prediction for the variation of interfacial area concentration along flow direction for 50.8mm diameter pipe

**7. Conclusion** 

(Hibiki, T. and Ishii, M. 2000a One-Group Interfacial Area Transport of Bubbly Flows in Vertical Round Tubes, International Journal of Heat and Mass Transfer, 43, 2711-2726.Fig.9)

In this chapter, intensive review on recent developments and present status of interfacial area concentration and its transport model was carried out. Definition of interfacial area and rigorous formulation of local instant interfacial area concentration was introduced. Using this formulation, transport equations of interfacial area concentration were derived in details. Transport equations of interfacial area concentration consist of conservation

Liquid flux jL=0.292 – 3.49 m/s, Gas flux jG=0.05098 –0.0931 m/s

#### **Condition II**

Pipe diameter D: 50.8mm, Measuring positions z from inlet: (z/D=6,30.3, 53.5)

Liquid flux jL=0.491 – 5.0 m/s, Gas flux jG=0.0556 –3.9 m/s

Figures 13 and 14 show the result of comparison between experimental data and prediction using transport equation of interfacial area with sink term due to bubble coalescence (Eq.(70)) and source term due to bubble break up (Eq.(72)). Predictions agree with experimental data within 10% accuracy.

Fig. 13. Comparison between Experimental data and prediction for the variation of interfacial area concentration along flow direction for 25.4mm diameter pipe (Hibiki, T. and Ishii, M. 2000a One-Group Interfacial Area Transport of Bubbly Flows in Vertical Round Tubes, International Journal of Heat and Mass Transfer, 43, 2711-2726.Fig.8)

Figures 13 and 14 show the result of comparison between experimental data and prediction using transport equation of interfacial area with sink term due to bubble coalescence (Eq.(70)) and source term due to bubble break up (Eq.(72)). Predictions agree with

Liquid flux jL=0.292 – 3.49 m/s, Gas flux jG=0.05098 –0.0931 m/s

Liquid flux jL=0.491 – 5.0 m/s, Gas flux jG=0.0556 –3.9 m/s

experimental data within 10% accuracy.

Pipe diameter D: 50.8mm, Measuring positions z from inlet: (z/D=6,30.3, 53.5)

Fig. 13. Comparison between Experimental data and prediction for the variation of interfacial area concentration along flow direction for 25.4mm diameter pipe

(Hibiki, T. and Ishii, M. 2000a One-Group Interfacial Area Transport of Bubbly Flows in Vertical Round Tubes, International Journal of Heat and Mass Transfer, 43, 2711-2726.Fig.8)

**Condition II** 

Fig. 14. Comparison between Experimental data and prediction for the variation of interfacial area concentration along flow direction for 50.8mm diameter pipe (Hibiki, T. and Ishii, M. 2000a One-Group Interfacial Area Transport of Bubbly Flows in Vertical Round Tubes, International Journal of Heat and Mass Transfer, 43, 2711-2726.Fig.9)

#### **7. Conclusion**

In this chapter, intensive review on recent developments and present status of interfacial area concentration and its transport model was carried out. Definition of interfacial area and rigorous formulation of local instant interfacial area concentration was introduced. Using this formulation, transport equations of interfacial area concentration were derived in details. Transport equations of interfacial area concentration consist of conservation

Transport of Interfacial Area Concentration in Two-Phase Flow 119

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**Thermal Aspects of Conventional** 

Wargha Peiman, Igor Pioro and Kamiel Gabriel

*University of Ontario Institute of Technology* 

*Canada* 

**and Alternative Fuels in SuperCritical** 

**Water-Cooled Reactor (SCWR) Applications** 

The demand for clean, non-fossil based electricity is growing; therefore, the world needs to develop new nuclear reactors with higher thermal efficiency in order to increase electricity generation and decrease the detrimental effects on the environment. The current fleet of nuclear power plants is classified as Generation III or less. However, these models are not as energy efficient as they should be because the operating temperatures are relatively low. Currently, a group of countries have initiated an international collaboration to develop the next generation of nuclear reactors called Generation IV. The ultimate goal of developing such reactors is to increase the thermal efficiency from what currently is in the range of 30 - 35% to 45 - 50%. This increase in thermal efficiency would result in a higher production of electricity compared to current Pressurized Water Reactor (PWR) or Boiling Water Reactor

The Generation IV International Forum (GIF) Program has narrowed design options of the nuclear reactors to six concepts. These concepts are Gas-cooled Fast Reactor (GFR), Very High Temperature Reactor (VHTR), Sodium-cooled Fast Reactor (SFR), Lead-cooled Fast Reactor (LFR), Molten Salt Reactor (MSR), and SuperCritical Water-cooled Reactor (SCWR). These nuclear-reactor concepts differ in their design in aspects such as the neutron

A SuperCritical Water-cooled Reactor can be designed as a thermal-neutron-spectrum or fast-neutron-spectrum system. SCWR operates above the critical point of water which is at a temperature of 374°C and a pressure of 22.1 MPa. The operating pressure of SCWR is 25 MPa and the outlet temperature of the coolant is 550 - 625°C depending on the design chosen by the respective country that is developing it. The primary choice of fuel for SCWR is an oxide fuel while a metallic fuel has been considered as the secondary choice for the fast-neutron-spectrum SCWRs. A supercritical-water Rankine cycle has been chosen as the power cycle (US DOE, 2002). The thermal efficiency of SCWR is in the range of 45 – 50 %.

Some of the advantages of SCW Nuclear Power Plants (NPPs) over the conventional NPPs include higher thermal efficiency within a range of 45−50% (Pioro and Duffey, 2007) compared to 30 – 35% for the current NPPs, lower capital costs per kWh of electricity, and the possibility

spectrum, coolant, moderator, and operating temperature and pressure.

Figure 1 shows a schematic diagram of a SCWR.

**1. Introduction** 

(BWR) technologies.

Zeitoun, O., and Shoukri, M., 1996 Bubble behavior and mean diameter in subcooled flow boiling, Transactions of the ASME, Journal of Heat Transfer, 118, 110-116. **7** 
