Thermal-Hydraulic Behavior during Reactor Accidents

Scale effects between reactors and integral effect test facilities

For installing or restarting nuclear reactors, various accidents are simulated using safety analysis codes to confirm safety. As a validation of the code, simulated accidents performed by the integral effect test facilities are analyzed, but the difference of size and condition between the reactor and the test, so called scale effect, is always a matter of concern.

Figure 1 shows the results of LSTF test, RELAP5 code analysis, and PWR analysis under the same conditions for the loss-of-coolant accident with a failure of HPI system. By developing the analytical model for the PWR and the test with the same modeling procedure and parameters, it was found that the transient behavior was almost the same, and the scale effect was small. [NUTHOS-12, 2018]

Fig.1
Fig.1 Analysis of Loss-of-Coolant accident: Primary pressure

BWR station blackout accident

The thermal-hydraulic behavior and effectiveness of operator action during accidents are studied using safety analysis codes.

The analysis of station blackout accident using the TRAC code showed that the thermal-hydraulic behavior of the Fukushima Daiichi Nuclear Power Plant up to the melting of the core could be well reproduced, and the timing and time margin of operator actions were examined. Based on this, we investigated the pressure rise inside the containment vessel and clarified the effects of leakage due to structural damage, which was controversial after the accident. Figure 2 shows that the containment pressure increased gradually by assuming the leakage or external cooling, and it was found that the reactor thermal-hydraulic behavior was not affected. [Annals of Nucl. Energy, 49 (2012) 223]

Fig.2
Fig.2 Analysis of station blackout accident: Containment pressure

PWR steam generator tube rupture accident

The injection of ECCS water during accidents is necessary for cooling, but the pressurized thermal shock is a matter of concern from the view point of structural integrity. The effectiveness and flow behavior of injected water are thus investigated.

Figure 3 shows the cold-leg fluid temperature during the steam generator tube rupture accident obtained by RELAP5. The effect of upper plenum injection at the same time as the cold-leg injection performed in the Mihama Unit 2 accident was investigated. In the base case, both were present, in case I, only the cold leg, in case II, none, in case III, the upper plenum injection is added to the cold leg. It was clarified that the effect of the upper plenum injection was small, and that the temperature dropped significantly only by the cold-leg injection. [Int. J. of Mech. Aero, Industrial, Mechatronic and Manufacturing Eng., 9 (2015) 1439]

Fig.3
Fig. 3 Analysis of steam generator tube rupture accident: Cold-leg fluid temperature in broken loop

Natural circulation in PWR steam generator

During PWR accidents, cooling is expected to continue due to the natural circulation. However, in steam generators equipped with a large number of U tubes, reverse flow may occur in some of the tubes, affecting cooling characteristics.

Figure 4 is a theoretically obtained stability map showing whether stable forward flow can be maintained. The solid line indicates the stability condition, and the symbol indicates the U-tube condition. If it is in the area above the solid line, a stable forward flow is established. The stagnant flow in long tubes revealed the stable forward flow in short tubes, and this condition was consistent with the experimental observations. [Annals of Nucl. Energy, 60 (2013) 344]

Fig.4
Fig. 4 Analysis of steam generator flow instability: Stability map

Coupling of CFD code and safety analysis code

In order to investigate the conditions under which natural circulation stops, a small loop test was used to simulate the situation where reverse flow occurs in a part of the U tubes. The entire loop flow was analyzed using RELAP5 and the individual U-tube flows were analyzed using the three-dimensional CFD code FLUENT, and the method for coupling the two analyses was established.

Figure 5 shows the temperature distribution and velocity vector near the entrance of the U tubes as a part of the 3D analysis. It was confirmed that reverse flow and stagnation occurred in some U tubes even under conditions where natural circulation was established in the entire loop, and it was also found that ascending and descending flows appeared simultaneously inside a single U tube. The stability of natural circulation was found to be a complicated flow phenomenon, rather than a simple forward and backward flow phenomenon in each tube, as previously thought. [Annals of Nucl. Energy, 70 (2014) 141]

Fig.5
Fig. 5 Analysis of steam generator flow instability: Temperature and velocity distributions

Critical flow from a crack

Before loss of coolant accidents, the leak-before-break phenomenon is an important concept for the structural integrity. Due to the high temperature and high pressure of the reactor, the leakage from cracks is a critical two-phase flow, but flow rate evaluation has been performed using a simple model so far.

Figure 6 shows the relationship between the equivalent diameter of the crack and the leakage flow rate obtained by typical critical flow models (HF model, RT model) using RELAP5 and compared with the simple model (Moody model). The two downward-sloping dotted lines show the flow rate assuming a detectable leak rate. The intersection with the upward-sloping curve by the critical flow model becomes the leak rate in the structural evaluation. The simple model was found to give the largest equivalent diameter at the intersection, and the most conservative result. [Int. J. Nucl. Quantum Eng., 13 (2019) 516]

Fig.6
Fig. 6 Analysis of leak flow through cracks: Two-phase critical flow rate vs. crack size

Fluid Physics of Droplet

Boundary-layer flow on the surface of a levitated droplet

The properties of high-temperature molten materials are necessary not only for severe accident analyses but also for developing new materials. However, normal measurement using a container is difficult at high temperatures where core melting occurs. Therefore, we are developing technology to measure physical properties from the shape vibration and rotation using levitated droplets.

Some kind of external force is required to levitate the droplets on the ground. It was found that the technique using ultrasonic waves induces a characteristic flow in a thin layer near the surface. Figure 7 shows the flow near the surface during one period of ultrasonic wave obtained by in-house CFD code. The blue part is the droplet side and the red part is the gas side. The surface flow was found to be countercurrent to the flow inside and outside the droplets at certain timings of one period. [Int. J. Multiphysics, 7 (2013) 19-30]

Fig.7
Fig.7 Analysis of levitated liquid droplet: Surface flow on droplet in acoustic standing wave

Viscosity measurement using rotating droplets

The method of obtaining viscosity from the rotating droplets uses the shape variation from a sphere to a dumbbell via a spheroid. Figure 8 shows how the shape varies due to rotation. It was clarified by the in-house CFD code that the relationship between the rotation rate and the elongation agreed with the experiment, and that two vortices were formed in the dumbbell. [Physical Review Fluids 5 (2020)083607].

Fig.8
Fig.8 Transient variations of droplet shape and velocity vector

Sodium droplet combustion

During the accidents of fast breeder reactors, there is a concern from the viewpoint of containment integrity that the coolant sodium leaks and forms droplets, and burns violently. In previous analyses, sodium droplets are treated as solids and only the surrounding combustion fields are examined. We thus treated the droplets as fluids, and the effects of combustion reactions on the flow fields are investigated.

Figure 9 shows the analysis of the combustion experiment using suspended droplets by introducing the combustion reaction model into the CFD code FLUENT. The upper part shows the pressure distribution and the lower part the velocity vector. The pressure distribution according to the shape and the formation of internal vortices due to surface tension were clarified. [WSEAS Trans. Heat Mass Trans., 14 (2019) 38]

Fig.9
Fig.9 Analysis of sodium droplet combustion: Pressure distribution (upper) and velocity vector (lower)