The parallel-plate channel, which simulates a single subchannel in a fuel assembly, was adopted as the computational domain, as shown in Fig. 1. Both plates were heated with a uniform heat flux of 270 kW/m2. The single-phase water flows into the parallel-plate channel vertically from the inlet. The hydraulic diameter and heated length of the computational domain are equal to those of the single subchannel in the fuel assembly of a current BWR. The outlet pressure of 7.1 MPa, the inlet velocity of 2.2 m/s, and the inlet temperature of 549.15 K also reflect the operating conditions in the current BWR. The adiabatic wall region is set up on the top of the heated region in order to eliminate the influence of the outlet boundary condition. In this analysis, the maximum bubble diameter in Eq. (8) is set to the channel width of 8.2 mm.

First, an analysis was performed without applying oscillation acceleration. After a steady boiling flow was attained, oscillation acceleration was applied. The time when the oscillation acceleration was applied is regarded as t = 0 s.

Fig. 1. Computational domain

Two cases of oscillation acceleration, in the vertical direction (Z axis) and in the horizontal direction (X axis), were applied. In both cases, the oscillation acceleration was a sine wave with a magnitude of 400 Gal and a period of 0.3 s, as shown in Fig. 2. The magnitude and period of the oscillation accelerations were taken from actual earthquake acceleration data.

Fig. 2. Time variation in oscillation acceleration

Figure 3 shows distribution of the void fraction at t = 0 s. Much of the void fraction was distributed near the wall at Z = 2.0 m, because the effect of the lift force was dominant at this time, and the lift force acted toward the wall. On the other hand, much of the void fraction was distributed in the center of the channel at Z = 3.66 m, because the effect of bubble deformation on evaluation of lift force was dominant, and the lift force acted toward the center of the channel.

Fig. 3. Void fraction distribution at t = 0 s

The case of horizontal oscillation acceleration is shown in Fig. 4, which shows the time variation in the void fraction at Z = 2.0 m and Z = 3.66 m. The void fraction fluctuated in the horizontal direction with the same period as the oscillation acceleration; however, it moved in the direction opposite to the oscillation acceleration at both Z = 2.0 m and Z = 3.66 m.

Figure 5 shows the time variation in the horizontal velocity of liquid and vapor at Z = 2.0 m, where a positive value of velocity corresponds to the positive direction along the X axis, and a negative value of velocity corresponds to a negative direction along the X axis. The liquid velocity fluctuated in the same direction as the oscillation acceleration, while the vapor velocity fluctuated in the opposite direction. These tendencies in liquid and vapor velocities at Z = 2.0 m can also be seen at Z = 3.66 m. If oscillation acceleration is applied in the horizontal direction, a horizontal pressure gradient arises in a direction opposite to that of
the oscillation acceleration in boiling flow. In this case, the liquid phase is driven by the oscillation acceleration because the influence of the oscillation acceleration is relatively large owing to a high liquid density; on the other hand, the vapor phase is driven by the horizontal pressure gradient because the influence of the oscillation acceleration is less than that of the horizontal pressure gradient owing to the low vapor density. This explains why the vapor velocity and the void fraction moved in a direction opposite to that of the oscillation acceleration.

(b) Z=3.66 m

Fig. 4. Time variation in void fraction in the horizontal oscillation acceleration case

Fig. 5. Time variation in liquid and vapor velocities in the horizontal oscillation acceleration case

The case of vertical oscillation acceleration is shown in Fig. 6, which also shows the time variation in the void fraction at Z = 2.0 m and Z = 3.66 m. The distribution of the void fraction at Z = 2.0m and Z = 3.66 m fluctuated with the same period as that of the oscillation
acceleration. The vertical oscillation acceleration caused fluctuations in the pressure in the channel, causing expansion and contraction of the vapor phase. This explains why the void fraction fluctuated with the same period as that of the oscillation acceleration.

A comparison between Fig. 4 and Fig. 6 indicates that the magnitude of the void fraction fluctuation for the horizontal oscillation acceleration case was greater than that for the vertical oscillation acceleration case at any vertical position.

It can therefore be confirmed that the fluctuation of the void fraction with the same period as the oscillation acceleration can be calculated in the case of both horizontal and vertical oscillation acceleration.

t= 1.2s

t = 0.9s t = 0.6s t = 0.3s t = 0.0s

variation in void fraction in the vertical oscillation acceleration case

1.2 Investigation of the effect of oscillation period on boiling two-phase flow behavior

The computational domain and thermal hydraulic conditions are the same as those for boiling two-phase flow in the parallel-plate channel, as described in the preceding section. The oscillation acceleration was applied at t = 0 s, after steady boiling flow was obtained.

Nine cases of oscillation acceleration, as shown in Table 1, were applied in order to investigate the influence of the oscillation period of the oscillation acceleration upon the boiling two-phase flow behavior. As shown in the preceding section, the influence of the horizontal oscillation acceleration upon boiling flow was greater than the influence of the vertical oscillation acceleration. Therefore, only the horizontal oscillation acceleration was investigated in these analyses. The minimum oscillation period of 0.005 s, as listed in Table 1, is equal to half of the minimum time interval of structural analysis in a reactor. The maximum oscillation period of 1.2 s is almost equal to the computable physical time of about 1 s. In all cases, magnitude of the oscillation acceleration was set to 400 Gal. Case G in Table 1 is the same as the horizontal oscillation acceleration case shown in section 2.3.

Case	Oscillation period
A	0.005 s
B	0.01 s
C	0.02 s
D	0.04 s
E	0.08 s
F	0.15 s
G	0.3 s
H	0.6 s
I	1.2 s

Table 1. Computational cases

Case I

Figure 8 shows the standard deviation distribution of void fraction fluctuation. In cases where the oscillation period is less than 0.01 s, the influence of the oscillation acceleration is small because the magnitude of the void fraction fluctuation is very small compared to that in the cases where the oscillation period is greater than 0.02 s. When the oscillation period is greater than 0.02 s, although the magnitude of the void fraction fluctuation increases with elevation, it decreases near the top of the heated region.

In cases where the oscillation period is between 0.02 s and 0.30 s, the standard deviation distributions varied significantly with the variation in the oscillation period. In Case F, the magnitude of the void fraction fluctuation was highest locally. Therefore, the distribution of void fraction fluctuation was significantly dependent on the oscillation period in this range.

Case A Case B Case C Case D Case E Case F Case G Case H Fig. 8. Standard deviation distribution of void fraction distribution

On the other hand, in cases where the oscillation period was greater than 0.30 s, the standard deviation distributions hardly varied with the variation in the oscillation period. Therefore, the influence of the oscillation acceleration is small in this range.

From the information above, it can be confirmed that the boiling two-phase flow analysis, which is consistent with the time-series data of oscillation acceleration and has a time period greater than 0.01 s, can be performed. This is because oscillation acceleration with an oscillation period of less than 0.01 s has very little influence on the boiling two-phase flow. In addition, the time variations in the void fraction in cases where the oscillation period is greater than 0.30 s are close to quasi-steady variation. This means that the computable physical time of about 1 s is enough to evaluate the response of the boiling two-phase flow to the oscillation acceleration. Therefore, it can be confirmed that effective analysis can be performed by extracting an earthquake motion of about 1 s at any time during an earthquake.