**3.1.3 Bubbly and slug flow in square duct**

By two-phase correlations for fluid mixing phenomena, volume or mass cross flow rate or mixing coefficients are evaluated. Then volume and mass conservation of two-phase flow is important function. As mentioned above, volume conservation equations for both phases are not solved, and the TPFIT has no special treatment to keep volume conservation. Then we must check volume conservation of the TPFIT. In two-phase flow fluid mixing phenomena, the maximum value of mixing gas flow rate is around 10% of gas flow rate in flow channel. An error of the volume conservation must be done below 1% if we want to predict mixing coefficient with accuracy of less than 10%.


Table 2. Numerical condition for bubbly flow in square duct.

Development of Two-Phase Flow Correlation

0.005

for Fluid Mixing Phenomena in Boiling Water Reactor 297

gas was also large. Then, large fluctuation of *Evol* in Case 1 and 2 was observed. However, except these fluctuations, the maximum value of volume conservation error: *Evol* were less than 0.2%. Therefore, it was confirmed that the TPFIT has enough performance of volume

0 0.05 0.1 <sup>−</sup>0.005

In the next step, we must validate TPFIT for fluid mixing phenomena. To evaluate TPFIT performance for two-phase flow fluid mixing phenomena between the subchannels,

TPFIT code was applied to 2-channel air-water mixing tests (Yoshida, 2007). The dimension of calculated test channel is shown in Fig.10 (a). The test channel, which consists of two parallel subchannels with an 8×8 mm square cross section and the interconnection, is 220 mm long and air and water flow upwards in it. The interconnection's gap clearance, horizontal and vertical length are 1.0 mm, 5.0 mm and 20 mm respectively. An irregular mesh division in the Cartesian system was adopted and two subchannels and the interconnection were formed by using obstacles as shown in Fig.11. The total number of effective control volumes was 428,680 respectively. The fluid mixing was observed at interconnection in the experiments. A non-slip wall, constant exit pressure and constant inlet velocity were selected as boundary conditions for each subchannel. The time step was controlled with a typical safety factor of 0.2 to keep it lower than the limitation value given by the Courant condition and stability condition of the CSF model. Calculation conditions

Fig. 9. Evaluated volume conservation error for two-phase flow in square duct.

numerical simulations for two-phase flow fluid mixing tests were performed.

**3.2 Verification for fluid mixing phenomena by experimental data** 

t [s]

Case 1 Case 2 Case 3 Case 4

conservation to simulate two-phase flow fluid mixing phenomena.

0

EVol[−]

**3.2.1 Air-water fluid mixing test** 

are shown in Table 3.

To check volume conservation, the TPFIT was applied to bubbly and slug flow in square duct. Numerical domain is shown in Fig.8 (a), and numerical conditions are shown in table 2. In the simulations, air-water and steam-water two-phase flow were used. Air-water twophase flow at atmospheric pressure is used as working fluid in many experimental researches, and the TPFIT was applied to these experiments for validation. Then we used in this simulation. Steam-water two-phase flow at 7.2MPa and 560K (saturation temperature at 7.2MPa) is appeared in real (actual) reactor conditions. Two-phase flow correlations will be checked or examined at this conditions, we also used in this simulation. On all walls, nonslip boundary condition was assigned, and inlet velocity and volume fraction of liquid were fixed. Outlet pressure was also fixed at atmospheric pressure or 7.2MPa.

Fig. 8. Numerical domain and example of interface shape.

Figure.8 (b) shows example of interface shapes. Different two-phase flows were formed in a square duct by the difference in inlet volume fraction. And complicated interface shapes were observed in higher volume fraction case (Case 1). Figure 9 shows evaluated volume conservation error. In this figure, *Evol* was volume conservation error and defined as following equation.

$$E\_{\rm vol} = \frac{Vol\_{\rm g}}{Vol\_{\rm g,in}} - \mathbf{1}\_{\rm \text{\textdegree}} \tag{16}$$

where *Volg* is calculated total gas volume in a square duct by use of simulated results. And *Volg,in* is total gas volume calculated by use of inlet condition of simulations:

$$\text{Vol}\_{\text{g.in}} = \mathcal{a}\_{\text{in}} \cdot w\_{\text{in}} \cdot \text{A:t} \tag{17}$$

where, A is area of square duct (=14×14=196mm2), t is time. In Case 1 and 2, differences between gas density and liquid density was relatively large, and effects of compressibility of

To check volume conservation, the TPFIT was applied to bubbly and slug flow in square duct. Numerical domain is shown in Fig.8 (a), and numerical conditions are shown in table 2. In the simulations, air-water and steam-water two-phase flow were used. Air-water twophase flow at atmospheric pressure is used as working fluid in many experimental researches, and the TPFIT was applied to these experiments for validation. Then we used in this simulation. Steam-water two-phase flow at 7.2MPa and 560K (saturation temperature at 7.2MPa) is appeared in real (actual) reactor conditions. Two-phase flow correlations will be checked or examined at this conditions, we also used in this simulation. On all walls, nonslip boundary condition was assigned, and inlet velocity and volume fraction of liquid were

fixed. Outlet pressure was also fixed at atmospheric pressure or 7.2MPa.

4.67

14.00

Inlet B

*y*

*y*

14.00

Inlet A

*x*

(a) Numerical Domain (b) Example of Interface shape

Figure.8 (b) shows example of interface shapes. Different two-phase flows were formed in a square duct by the difference in inlet volume fraction. And complicated interface shapes were observed in higher volume fraction case (Case 1). Figure 9 shows evaluated volume conservation error. In this figure, *Evol* was volume conservation error and defined as

> , 1 *<sup>g</sup>*

*Vol*

*Vol*

where *Volg* is calculated total gas volume in a square duct by use of simulated results. And

, · ·· *V w g in i in <sup>n</sup> o t l A* 

where, A is area of square duct (=14×14=196mm2), t is time. In Case 1 and 2, differences between gas density and liquid density was relatively large, and effects of compressibility of

*g in*

*vol*

*E*

*Volg,in* is total gas volume calculated by use of inlet condition of simulations:

Case 1 Case 2

, (16)

, (17)

*x*

14.00

following equation.

*z*

*x*

Fig. 8. Numerical domain and example of interface shape.

gas was also large. Then, large fluctuation of *Evol* in Case 1 and 2 was observed. However, except these fluctuations, the maximum value of volume conservation error: *Evol* were less than 0.2%. Therefore, it was confirmed that the TPFIT has enough performance of volume conservation to simulate two-phase flow fluid mixing phenomena.

Fig. 9. Evaluated volume conservation error for two-phase flow in square duct.
