An experimental investigation of subcooled choked flow in a steam generator tube crack (P1)
In a pressurized water reactor (PWR), steam generators (SG) are heat exchangers used to turn water into steam from the heat produced in the nuclear reactor core. They make up a large fraction of the pressure boundary surface in the reactor primary coolant loop, while serving as a barrier to prevent fission products from entering the secondary side. Any leakage occurring on the wall of a SG tube will lead to the release of radioactive material from the primary coolant loop, which might eventually cause a leakage of radiation into the atmosphere. The integrity of a SG tube, therefore, plays an important role in nuclear power plant safety.
The SG tubes are designed to withstand high pressure differential while the nuclear reactor is in operation, e.g., 8.6 MPa (1247.3 psi) in PWR (Buongiorno, 2010). However, they are susceptible to corrosion and mechanical damage. There is a variety of degradations, which impair the SG tubes integrity and, therefore, increases the probability of the Loss of Coolant Accident (LOCA). One of the major mechanisms of SG tube failure is Stress-Corrosion Cracking (SCC) which occurs due to a combination of corrosive environment, susceptible material and a constant tensile stress on material. A comprehensive review on the mechanism, initiation and crack growth models of SCC was presented in the work of Vadlamani et al., (2012). This is considered as the most likely mode of failure which accounts for about 60% to 80% of all damage in SG tubing (Revankar et al., 2013).
SG tubes integrity assessment of a PWR requires a determination of potential degradation during operation. Sufficient safety criteria must be satisfied by each SG tube to maintain a suitable level of plant safety and reliability. A process called degradation assessment is employed as an initial step of the integrity assessment. The degradation assessment identifies degradation mechanisms which are required to select the appropriate examination techniques. The next steps are then condition monitoring and operation assessment performed during the refuel outage to ensure all the SG performance criteria are met (IAEA, 2007). An important concept in the integrity assessment is Leak Before Break (LBB). This concept is widely used to describe the idea that a leak will develop in the piping carrying the coolant before a disastrous break occurs (IAEA, 1993). The LBB concept demonstrates that a crack can grow through the tube wall and the leakage resulting from this crack would be detected by the leakage monitoring system before the tube ruptures. Application of the LBB concept could save a huge amount in construction and maintenance cost of a nuclear power plant. Most research in the SG tube integrity, therefore, characterized the burst of tubes with flaws (Keating et al., 1955). These studies were performed with the tube ultimately leading to burst (Kuchirka et al., 1997). The lack of break geometry characterization impairs benchmarking the predictions of leak rates through SG tube cracks with the experimental data.
The coolant is in subcooled state in the SG primary side, while it boils in the secondary side. As a leakage occurs on the SG tube wall, the coolant leaking from the primary side to the secondary side is subjected to high depressurization rate. Stagnation state of the coolant leakage flow is subcooled liquid and the flow reaches saturation pressure somewhere in the channel. For a given stagnation state and flow channel geometry, there is a maximum obtainable discharge flowrate. The flow is then said to be choked and the choking mass flux is a function of only the stagnation state and the channel geometry. Due to the rapid depressurization rate, the evolution of the flow from subcooled stagnation state to two-phase condition may lead to the formation of a metastable fluid phase (Amos and Schrock, 1983). The phenomenon was studied experimentally (Lienhard et al., 1978) and the result indicated that vaporization begins at a point which is well below the saturation pressure corresponding to the fluid temperature. In other words, the liquid can be superheated beyond the saturation temperature because two-phase depressurization speed is much faster than the thermal exchange rate between the two phases (Yoon et al, 2006).
Leak rate analysis of degraded tubes has currently attracted interest of many researchers. Lots of experimental works on choked flow with water-steam have been conducted. In the scope of this research, only studies on slit or crack geometries are mentioned. An experimental study, reported by Agostinelli et al., (1958), was done with annular, constant area passages with hydraulic diameters ranging from 0.15 to 0.43 mm. The experiment was conducted with water under pressures ranging from 3.5 to 20.5 MPa and subcooling from 9.30C to 670C. Simoneau (1974) performed a two-phase choked flow experiment with subcooled nitrogen flowing through a slit. The slit, a narrow rectangular passage of equal length and width, had the L/D (length to diameter ratio) of 43.5. The stagnation pressures were in a range up to 6.8 MPa and inlet temperature was studied over a range 0.84 < TR < 1.03, where TR is the ratio of inlet temperature to critical temperature. Abdollahian et al., (1983) carried out a study on two-phase critical (choking) flow through simulated and actual cracks. The experimental results were then used to validate the Battelle critical flow model and recommendations were made to improve the modelling assumptions. The experimental database was then developed by Collier et al., (1984). The study was focused on the effect of fluid pressure and temperature, crack geometry and crack surface roughness on the leak flow rate. The study used simulated cracks in which geometric conditions were carefully controlled and real intergranular stress corrosion cracks. An extensive experimental data was generated by Amos and Schrock (1983) for the choked flow of initially subcooled water through slits. The stagnation pressures in this study ranged from 4.1 to 16.2 MPa and the liquid subcoolings were in a range from zero to 650C. Frictional effects were shown to play an essential role in two-phase choked flow for the slit geometries characterized by large L/Ds. Homogeneous nonequilibrium model for two-phase choked flow, developed in this study, considers the effects of wall friction and delay of flashing flow. The model prediction was in a good agreement with the experimental data. John et al., (1988) carried out a detailed test with subcooled water under pressure up to 14 MPa. The experiment was done with both a real crack and simulated cracks and covered a wide range of stagnation pressure, liquid subcooling, slit width and inner surface roughness. More recent works were published by Bandyopadhyay et al., (2007) and Ghosh et al., (2011). These works were conducted with pipes containing circumferential slits created by Wire EDM. The authors observed different flow behavior in the tight slits with channel length as small as 8 mm compared to greater slit dimensions or longer flow channel. An experimental investigation of subcooling choked flow in simulated cracks was conducted by Revankar et al., (2013). The L/Ds of these cracks were in a range from 4.5 to 5.4 which are significantly smaller than that of previous works. Stagnation pressure was varied from 0.69 to 6.89 MPa and the liquid subcooling ranged from 200C to 500C. Homogeneous thermal non-equilibrium model was shown to improve the choking mass flux prediction of homogeneous thermal equilibrium model.
Despite the great number of experimental study on the choked flow through slit geometries, data on the SG tube leak rate measurement is still limited. Most of the works consists of long tubes with large L/Ds and nozzles. Although a large variety of pressures and liquid subcoolings was studied, the subcooled choked flow studies has been restricted to L/Ds greater than 15 (Revankar et al., 2013). Also, the experimental data are for channel lengths greater than 10 mm, which is not indicative of SG tubing. In view of this, an experimental program was conducted on choked flow of subcooled water through five samples of axial cracks on SG tubes. Three of them (sample 1, 2 and 4) were taken from the CANDU reactor. The other two samples (sample 3 and 5) resemble the SG tubes used in the US PWR. The present research studies the dependence of choked mass flux on the stagnation pressure, liquid subcooling and crack geometry to provide more insight on the choked flow in very short channel lengths characterizing the SG tubes.