**3.2.3 Numerical simulation of air-water two-phase flow in modeled 2 subchannels**

The TPFIT code was applied to experimental analyses of the existing 2-channel fluid mixing experiments (Sumida, 1995), and comparisons between measured and calculated results were carried. In the experiments, the differential pressure between the subchannel at the center height of the mixing section and the exit air and water flow rate of each subchannel were measured.

Numerical analyses of air-water flow fluid mixing were applied between the length of - 100mm and +60mm from the lower edge of the mixing section in the flow direction of the test channel as shown in Fig.17 (a). The flow area is divided into two channels by a flat plate (partition plate). At the upper part of the partition plate, there was a narrow slit, through which the channels were connected. The flow channel was divided into 3 parts, developing section, mixing section and outlet section. The narrow slit was located in the mixing section, and fluid mixing was occurred at this section. The developing section was set up to get developed flow at inlet of the mixing section. The outlet section was located at top of the calculated test channel to let out air-water two-phase flow smoothly.

Development of Two-Phase Flow Correlation

Fig. 18. Observed and calculated slug behavior of case H1.

degree of fluctuation of values was evaluated by the following equation:

Example of the calculated slug behaviors in the test channel are shown in Fig.18. As shown in Fig.18, the fluid mixing was observed at the gap between the subchannels. The measured and calculated differential pressure between the 2 subchannels is shown in Fig.19. The pressure differences at the longitudinal center of the mixing section were measured and calculated. In the figure, time averaged values ("Average") and standard deviation of fluctuating values ("Fluctuation" in the figure) of differential pressure are shown. The

cases".

for Fluid Mixing Phenomena in Boiling Water Reactor 303

constant, and the inlet air and water velocities were varied to simulate experimental conditions. Eight cases of air-water two-phase flow simulations were performed and calculation conditions were summarized in Table 5. In the simulation, inlet liquid mass flux for 2 subchannels was same. Outlet pressure and inlet temperature of air and water is set to atmospheric pressure and room temperature respectively. In the case H1 to H4, inlet liquid mass flux was set to 370 (kg/s), and inlet quality was relatively low. In the case H1 to 4, inlet liquid mass flux was set to 277 (kg/s), and inlet quality was relatively high. Then, we describe case L1 to L4 with "low quality cases", and case H1 to H4 with "high quality

Fig. 17. Dimensions of calculated test channel and calculation meshes in channel cross section for air-water two-phase flow.

Regular mesh division in the Cartesian system was adopted and two subchannels and the interconnection were formed by using obstacles as shown in Fig.17 (b). The calculation mesh size was set to 2/3 mm to satisfy the condition that the number of the calculation meshes of gap region must be more than 6, and the total number of the calculation meshes was 496,800. A non-slip wall, constant exit pressure and constant inlet velocity were selected as boundary conditions for each subchannel. The effects of the contact angle of the water on the channel walls were set to 15 degree.


Table 5. Air-water flow calculation condition.

Air and water were injected through the air and water inlet section located at lower part of the modeled test channel (see Fig.17 (a)). The area of the air and water inlet section was

(a) Calculated test channel (b) Calculation mesh

Fig. 17. Dimensions of calculated test channel and calculation meshes in channel cross

Regular mesh division in the Cartesian system was adopted and two subchannels and the interconnection were formed by using obstacles as shown in Fig.17 (b). The calculation mesh size was set to 2/3 mm to satisfy the condition that the number of the calculation meshes of gap region must be more than 6, and the total number of the calculation meshes was 496,800. A non-slip wall, constant exit pressure and constant inlet velocity were selected as boundary conditions for each subchannel. The effects of the contact angle of the water on

Case Inlet liquid mass flux (kg/m2s) Inlet quality (%)

L2 0.0013 L3 0.0019 L4 0.0026

H2 0.0022 H3 0.0033 H4 0.0044

Air and water were injected through the air and water inlet section located at lower part of the modeled test channel (see Fig.17 (a)). The area of the air and water inlet section was

Ch.1 Ch.2 Ch.1 Ch.2

0.0007

0.0011

370 0.0013

277 0.0022

Air

Developing section

*Slit* Mixing section

Channel 1 Channel 2

50

100

z

x

section for air-water two-phase flow.

the channel walls were set to 15 degree.

L1

H1

Table 5. Air-water flow calculation condition.

10

Outlet section constant, and the inlet air and water velocities were varied to simulate experimental conditions. Eight cases of air-water two-phase flow simulations were performed and calculation conditions were summarized in Table 5. In the simulation, inlet liquid mass flux for 2 subchannels was same. Outlet pressure and inlet temperature of air and water is set to atmospheric pressure and room temperature respectively. In the case H1 to H4, inlet liquid mass flux was set to 370 (kg/s), and inlet quality was relatively low. In the case H1 to 4, inlet liquid mass flux was set to 277 (kg/s), and inlet quality was relatively high. Then, we describe case L1 to L4 with "low quality cases", and case H1 to H4 with "high quality cases".

Fig. 18. Observed and calculated slug behavior of case H1.

Example of the calculated slug behaviors in the test channel are shown in Fig.18. As shown in Fig.18, the fluid mixing was observed at the gap between the subchannels. The measured and calculated differential pressure between the 2 subchannels is shown in Fig.19. The pressure differences at the longitudinal center of the mixing section were measured and calculated. In the figure, time averaged values ("Average") and standard deviation of fluctuating values ("Fluctuation" in the figure) of differential pressure are shown. The degree of fluctuation of values was evaluated by the following equation:

Development of Two-Phase Flow Correlation

*Wm*1: Inlet mass flow rate of m phase for channel 1 *Wm*2: Inlet mass flow rate of m phase for channel 2 *wm*: Moved mass flow rate from channel 1 to channel 2

insufficient spatial resolution when gas velocity is relatively low.

coalescence of bubbles/slugs caused by the interactions.

simulations were performed (see table 6 and 7).

**4.1.1 Analytical conditions** 

B1

**4.1 Evaluation of existing correlations for fluid mixing phenomena** 

1995):

where,

for Fluid Mixing Phenomena in Boiling Water Reactor 305

The measured and calculated mixing coefficients of both phases for air-water cases are shown in Fig.20. The mixing coefficients of gas and liquid are defined as below (Sumida,

*m*

1 2 *m*

(20)

*m m*

Underestimations tended to be made in cases of low inlet quality, but the numerical results agreed well the experimental results. These underestimations of mixing coefficients corresponded to those of differential pressure. It seems that a main cause of underestimations was overestimation of the flow resistance in the gap region due to

**4. Development of two-phase flow correlation for fluid mixing phenomena** 

Innovative water reactor for flexible fuel cycle (FLWR) is one of new generation light water reactor and has been developed at Japan Atomic Energy Agency (Uchikawa, 2007). In order to achieve a conversion ratio higher than unity, a hexagonal tight-lattice rod bundle with about 1mm of gap width was adopted. Due to narrower rod gaps and the channels being surrounded by rods, bubble/slug-to-bubble/slug and bubble/slug-to-wall interactions may occur more frequently within the FLWRs core than in those of current BWRs, and these may affect the two-fluid mixing characteristics by way of the deformation, separation and

In this section, to evaluate the existing two-phase flow correlation for fluid mixing phenomena, two-phase flow in 2 modeled subchannels for BWRs and FLWRs fuel bundles were performed ("BWR cases" and "FLWR cases"). For this, 16 cases of two-phase flow

Ch.1 Ch.2 Ch.1 Ch.2

0.0067

Case Inlet liquid mass flux (kg/m2s) Inlet quality (%)

0.0264 B2 0.0134

0.0362 B6 0.0362

Table 6. Calculation conditions for fluid mixing phenomena in BWRs fuel bundle.

1400

B3 0.0264 B4 0.0513 B5 0.0184

B7 0.0533 B8 0.0699

*w W W*

$$
\sigma\_{\Delta p} = \sqrt{\left(\Delta p\_{\tau} - \Delta p\_{s}\right)^{2}} \tag{18}
$$

where,

$$
\Delta p\_s = \Delta p\_\tau \tag{19}
$$

*pt*: instantaneous value of differential pressure.

*ps*: time averaged value of differential pressure

Underestimations tended to be made in cases of low inlet quality, but the numerical results agreed well with the experimental results, both qualitatively and quantitatively.

Fig. 19. Measured and calculated pressure difference between subchannels.

Fig. 20. Measured and calculated mixing coefficient.

The measured and calculated mixing coefficients of both phases for air-water cases are shown in Fig.20. The mixing coefficients of gas and liquid are defined as below (Sumida, 1995):

$$\Gamma\_m = \frac{w\_m}{\mathcal{W}\_{m1} + \mathcal{W}\_{m2}} \tag{20}$$

where,

304 Computational Simulations and Applications

Underestimations tended to be made in cases of low inlet quality, but the numerical results

(a) Low quality case (Case L1~L4) (b) High quality case (Case H1~H4)

(a) Low quality case (Case L1~L4) (b) High quality case (Case H1~H4)

0

(−)

0.5

Measured

Predicted

Fig. 19. Measured and calculated pressure difference between subchannels.

0

0.2

p (kPa)

0.4

Measured

Predicted

agreed well with the experimental results, both qualitatively and quantitatively.

*pt*: instantaneous value of differential pressure. *ps*: time averaged value of differential pressure

Average Fluctuation

0 0.5 1 1.5 2 2.5

X2/X1

Gas Liquid

0 0.5 1 1.5 2 2.5

X2/X1

Fig. 20. Measured and calculated mixing coefficient.

where,

0

0.4

0

0

(–)

0.5

Measured Predicted

0.2

p (kPa)

Measured

Predicted

 <sup>2</sup> *p TS*

*p p* (18)

*S T p p* (19)

Average Fluctuation

0.0 0.5 1.0 1.5 2.0 2.5

X2/X1

Gas Liquid

0.0 0.5 1.0 1.5 2.0 2.5

X2/X1

*Wm*1: Inlet mass flow rate of m phase for channel 1 *Wm*2: Inlet mass flow rate of m phase for channel 2

*wm*: Moved mass flow rate from channel 1 to channel 2

Underestimations tended to be made in cases of low inlet quality, but the numerical results agreed well the experimental results. These underestimations of mixing coefficients corresponded to those of differential pressure. It seems that a main cause of underestimations was overestimation of the flow resistance in the gap region due to insufficient spatial resolution when gas velocity is relatively low.
