**4. Conclusion**

172 Nuclear Reactors

Figure 17 shows the time variation in the Eotvos number at Z = 3.4 m and also shows a range of Eotvos number from 4 to 10 for which the effect of bubble deformation upon the lift force is dependent upon Eotvos number, as shown in Eq. (7). The black arrow shows the direction in which the oscillation acceleration acts. The red and blue circles in Fig. 17 correspond to regions where the magnitude of the lift force was large; the lift force acted in a direction facing away from the fuel rod surface, as shown in Fig. 16. In these regions, the effect of bubble deformation on the lift force was dominant because the Eotvos number exhibited high values. Near the fuel rod surface, the Eotvos numbers less than 4 and greater than 10 were mixed, indicating that the magnitude and direction of the lift force were not

(a) *t* = 0.78 s (*fx* = *fy* ≠ 0) (b) *t* = 0.8 s (*fx* = *fy* = 0) (c) *t* = 0.82 s (*fx* = *fy* ≠ 0)

(a) *t* = 0.78 s (*fx* = *fy* ≠ 0) (b) *t* = 0.8 s (*fx* = *fy* = 0) (c) *t* = 0.82 s (*fx* = *fy* ≠ 0)

Figure 18 shows the variation in bubble diameter with time at Z = 3.4 m. The black arrow shows the direction in which the oscillation acceleration acts. Bubble diameters greater than 7 mm are distributed in the region where the Eotvos number is greater than 10, as shown in Fig. 17. The bubble diameter distribution shown in Fig. 18 is strongly inhomogeneous and physically invalid because large bubble diameters are mainly observed in small regions in the subchannel, while small bubble diameters of less than 3 mm are observed in the center of the subchannel. This strongly inhomogeneous bubble diameter distribution resulted in

The region where large bubble diameters are seen corresponds to the region of high void fraction, as shown in Fig. 14. According to Eq. (8), the bubble diameter is significantly

locally high Eotvos numbers and fluctuation in the direction of the lift force vectors.

uniform near the fuel rod surface.

Fig. 16. Time variation in lift force vector at Z = 3.4 m

Fig. 17. Time variation in the Eotvos number at Z = 3.4 m

A new external force term, which can simulate the oscillation acceleration, was added to the momentum conservation equations in order to apply the three-dimensional two-fluid model analysis code ACE-3D under earthquake conditions.

A boiling two-phase flow excited by applying vertical and horizontal oscillation acceleration was simulated in order to confirm that the simulation can be performed under oscillation conditions. It was confirmed that the void fraction fluctuation with the same period as that of the oscillation acceleration could be calculated in the case of both horizontal and vertical oscillation acceleration.

The influence of the oscillation period of the oscillation acceleration on the boiling twophase flow behavior in a fuel assembly was investigated in order to evaluate the highest frequency necessary for the improved method to be consistent with the time-series data of oscillation acceleration and the shortest period of oscillation acceleration for which the boiling two-phase flow shows quasi-steady time variation. It was confirmed that a boiling two-phase flow analysis consistent with the time-series data of oscillation acceleration and with a time interval greater than 0.01 s, can be performed. It was also shown that an effective analysis can be performed by extracting an earthquake motion of about 1 s at any time during the earthquake.

The three-dimensional behavior of boiling two-phase flow in a fuel assembly under oscillation conditions was evaluated using a simulated fuel assembly excited by oscillation acceleration. On the basis of this evaluation, it was confirmed that void fraction fluctuation

**9** 

*Iran* 

**The Theoretical Simulation of a Model by** 

*Department of Physics, Islamic Azad University, South Tehran Branch, Tehran* 

**Dynamical Stability of Nuclear Reactors Cores** 

According to complexity of nuclear reactor technology, applying a highly developed simulation is necessary for controlling the nuclear reactor control rods, so in this proposal the processes of a controlling model for nuclear reactors have been developed and simulated by the SIMULINK tool kit of MATLAB software and all responses, including oscillation and

In this work an arbitrary value of Keff as a comparable value is purposed and attributed to input block (*H*) of diagram and then this value with the received feedback value from block diagram is compared. Since the stability of the cited simulation depends on either velocity or delay time values, therefore according to this simulation the best response and operation which a reactor can have from stability aspect, have been derived. Meantime by viewing the results, the best ranges of velocity and delay time of control rod movement (in unit per second and millisecond respectively) for stability a nuclear reactor has been

• Determination of the best ranges for both velocity and delay time of control rod movement (in unit per second and millisecond respectively) based on the obtained

In view of the great advancing the nuclear reactors technology, the phenomenal and significant changes in evolution of made nuclear reactors is observed. Since the make of the first nuclear reactor on 1948 until modern reactors, too changes are obvious. The major of these changes to: the kind of reactor design, the percent of fuel enrichment, the kind of

The power control system is a key control system for a nuclear reactor, which directly affects the safe operation of a nuclear reactor. Much attention has been spent to the power control

coolant and neutron moderator, more safety and the dimensions of core are referred.

system performance of nuclear reactor in engineering (Zhao et al., 2003).

Though the highlights of this proposal are respectively the following:

• Defining a mathematical model for control rod movement • Simulation of a mathematical model by SIMULINK of MATLAB

results for stability an LWR nuclear reactor

**1. Introduction** 

deduced.

transient responses, have been analyzed.

**SIMULINK for Surveying the Work and** 

Seyed Alireza Mousavi Shirazi

in the downstream region is significantly dependent on the lift force caused by a strongly inhomogeneous bubble diameter distribution and that it is necessary to adequately evaluate the influence of void fraction on bubble diameter in order to avoid strongly inhomogeneous bubble diameter distribution under oscillation conditions.

### **5. Acknowledgment**

The present study includes the result of "Research of simulation technology for estimation of quake-proof strength of nuclear power plant" conducted by the University of Tokyo as Core Research for Evolutional Science and Technology (CREST). This research was conducted using a supercomputer of the Japan Atomic Energy Agency.

#### **6. References**

