Safety | Simulation

Calculating LOCA system effects

14 February 2012



The ability of the Westinghouse FULL SPECTRUM LOCA™ (FSLOCA™) best-estimate code to adequately capture the phenomena most important and dominant for small, intermediate, and large breaks of the cold leg is demonstrated for a three-loop Westinghouse PWR. Nominal scenarios, in which typical values are assumed for uncertainty parameters, illustrate the influence of break size on the important system-level phenomena predicted by the code. By M. A. Shockling, C. Frepoli and K. Ohkawa.


Historically, loss-of-coolant accident (LOCA) analyses have considered large and small breaks separately. Differing important phenomena for the two classes of postulated events led to the use of separate safety analysis codes, each with its own set of important phenomena, validation basis, and analysis methodology. Since the mid-1990’s, best-estimate methodologies specific to large breaks have been developed and implemented by Westinghouse and others to better capture the plant response to a postulated break and to gain analysis margin. Recently, Westinghouse has developed the FULL SPECTRUM LOCA™ (FSLOCA™) methodology to address postulated breaks in a best-estimate manner ranging from the smallest to the largest break sizes [1].

US Regulatory Guide 1.203 [2] describes a process for developing and assessing evaluation models “used to analyze transient and accident behaviour that is within the design basis of a nuclear plant,” known as the Evaluation Model Development and Assessment Process (EMDAP). In developing the FSLOCA™ methodology, Westinghouse has followed such a process. The first step of the process identifies the purpose (LOCA analysis over the full spectrum of postulated break sizes), the transient class (best-estimate-plus-uncertainty accident analysis), and the power plant class (three-loop Westinghouse PWR). Step 2 specifies figures of merit, which for a LOCA analysis are the 10 CFR 50.46 criteria related to peak cladding temperature and cladding oxidation, but also require the evaluation model (EM) to demonstrate conservatisms related to important phenomena that influence the prediction of cladding temperatures and oxidation.

Step 3 and 4 of the EMDAP process involve the identification of systems, components, phases, geometries, fields and processes that should be modeled, and identify and rank the phenomena and processes that are deemed relevant. A Phenomena Identification and Ranking Table (PIRT) process is used to list processes of importance and indicate at what times in the transient each process occurs. A single PIRT has been developed for the FSLOCA™ methodology, following the approach outlined in [3], as discussed by [4].

Westinghouse has previously developed both large break and small break LOCA PIRTs, and these PIRTs were the subject of NRC review (for the large-break LOCA PIRT) and independent peer review (for the small-break LOCA PIRT). Relative rankings in the recently developed FSLOCA™ PIRT were assigned into four categories: high, medium and low importance, and not applicable. It is crucial that items ranked highly important (‘H’) be modelled accurately to correctly predict the transient.

This paper focuses on the observation of a few of the highly-ranked phenomena in the context of typical small break (SB), intermediate break (IB), and large break (LB) LOCA transients postulated to occur in the cold leg of a typical 3-loop Westinghouse pressurized water reactor (PWR). Postulated pipe breaks range from very small sizes (split, or longitudinal ruptures) up to and including a full double-ended guillotine (DEG) break of the largest pipe in the circuit, in which it is postulated that the pipe is completely and instantaneously severed, with no interaction between the two break planes. A systematic evaluation of the code’s capability in accurately modelling the phenomena is provided in [1] and goes beyond this article.

An element of the EMDAP process is to specify the transient periods of interest to identify the relevant phenomena for each. A realistic code intended to analyze the full spectrum of breaks must be capable of predicting the major phenomena that influence the system response and bring about the main characteristics of the transient. These characteristics differ quite significantly over the postulated range of break sizes, and the importance of phenomena varies throughout the transient as well. Below, the periods for small, intermediate, and large break LOCAs are defined, and a demonstration of the predicted transient is provided.

Small Break LOCA (SBLOCA)

1. Blowdown: Upon initiation of the break, there is a rapid depressurization of the primary side of the reactor coolant system (RCS). Reactor trip is initiated on a low pressurizer pressure setpoint (approximately 1860 psia). Loss of condenser steam dump effectively isolates the steam generator (SG) secondary side, causing it to pressurize to the safety valve setpoint (approximately 1100 psia) and release steam through the safety valves. A safety injection (SI) signal occurs when the primary pressure decreases below the pressurizer low-low pressure setpoint (approximately 1760 psia), and SI begins after some delay time. The RCS remains nearly single-phase liquid for most of the blowdown period, with phase separation starting to occur in the upper head, upper plenum, and hot legs near the end of this period. During the blowdown period, the break flow is single-phase liquid. Eventually, the entire RCS saturates, the rapid depressurization ends, and the RCS reaches a pressure just above the SG secondary side pressure. Some phenomena ranked ‘H’ during this phase of a SBLOCA include the prediction of single- and two-phase critical flow through the break and the decay heat in the core, since they influence directly the rate of inventory loss and depressurization and drive the cladding heat-up, respectively.

2. Natural circulation: At the end of the blowdown period, the RCS pressure reaches a quasi-equilibrium condition that can last for several hundred seconds, during which the SG secondary side acts as a heat sink. During this period, the system drains from the top down, with voids beginning to form at the top of the SG tubes and continuing to form in the upper head and top of the upper plenum regions. There is still adequate liquid to allow significant natural circulation two-phase flow around the loops; decay heat is removed through condensation in the SGs during this time. Significant coolant mass depletion continues from the RCS, and vapour generated in the core is trapped within the upper regions by liquid plugs in the loop seals (the U-shaped section in the cold leg between the steam generator outlet plenum and the reactor coolant pump inlet), while a low-quality flow still exits the break. Critical flow at the break remains a highly-ranked phenomenon during this phase, as it influences the rate of inventory depletion.

3. Loop seal clearance: When the liquid level in the downhill side of the pump suction piping is depressed to the bottom of the loop seal, steam previously trapped in the RCS can be vented to the cold leg break. The break flow, previously a low-quality mixture, transitions to primarily steam. Prior to loop seal venting, the static head balances within the RCS can cause the vessel collapsed mixture level (the level of liquid excluding vapour) to depress into the core, potentially allowing the cladding to heat up. Following the venting, the vessel level recovers to about the cold leg elevation, as the imbalances throughout the RCS are relieved. Some phenomena ranked ‘H’ during this phase include the prediction of horizontal stratification and interfacial drag in the loop seal, since they influence the timing of the loop seal clearance.

4. Boiloff: Following loop seal venting, the vessel mixture level continues to decrease due to the boiloff of the remaining liquid inventory, since the RCS pressure is generally still too high to allow sufficient emergency core cooling system (ECCS) injection by the high-pressure SI pumps. The mixture level will reach a minimum, in some cases resulting in core uncovery, before the RCS has depressurized to the point where the break flow becomes lower than the rate of ECCS water delivery. The prediction of voids and mixture level in the core is important during this phase for reasonable prediction of cladding temperature excursions related to core uncovery.

5. Core recovery: The vessel mass inventory is replenished from its minimum with ECCS water, and the core recovers. The transient is terminated once the entire core is quenched and the pumped SI flow exceeds the break flow. Typically the vessel inventory depletion will end once the RCS depressurizes to the accumulator check valve pressure (for this reactor type, 600-700 psi, 4.14-4.83 MPa), at which point the insurge of cold liquid quenches the rods.

A proxy for determining the periods of a SBLOCA transient is the system pressure. Typically, the RCS pressure will quickly reduce immediately following the break initiation during blowdown. The end of blowdown is evident from a stabilization of pressure over a significant amount of time, during natural circulation. Loop seal clearance marks the beginning of the boiloff period, marked by a monotonically reducing system pressure. As core recovery occurs, the pressure stabilizes to a new quasi-equilibrium dictated by the flow resistances in the system and at the break. Figure 1 shows the prediction for cold leg breaks ranging from 2.0 to 8.0 inches (51 mm to 203 mm) in diameter.

To demonstrate the prediction of highly-ranked phenomena, the 3-inch break is explored here in further detail. Figure 2 shows the predicted pressurization of the steam generator secondary side, and the depressurization of the RCS, within the first ~20-50 seconds of the transient. A quasi-equilibrium is sustained for around 1000 seconds during the natural circulation phase, where the SG secondary side remains below the RCS pressure, indicating that it is a heat sink. Until the loop seal clearance occurs and a vapour vent path is established, the break flow remains two-phase (Figure 3). For this demonstration, a homogeneous non-equilibrium relaxation critical flow model [5] was used to predict break flow and pressure losses, which, as described in the previous section, is a highly-ranked phenomenon.

A realistic LOCA evaluation model intended to analyze SBLOCA must address the phenomenon of loop seal clearance. Loop seal clearance has been demonstrated to be a highly variable event characterized by ‘phenomenological uncertainty’ [6] associated with flow stratification, interfacial drag, flow slugging, and instabilities caused by small differences among the intact and broken loops. For very small breaks, either no loop seals will clear or the broken loop will clear ‘preferentially due to its proximity with the break’ [6]. Relatively large breaks will exhibit multiple loop seal clearance, a process associated with oscillations, and the loops that do clear tend to be random. Such a situation is observed for the 3-inch break, shown in Figure 4; the two intact loops exhibit full loop seal clearance (indicated by a differential pressure near zero, constant after ~1000s), while the broken loop only partially clears. Although not shown here, other transients made it apparent that the phenomenological uncertainty described by [6] is generally observed with the FSLOCA™ code.

As shown in Figure 3, the break flow after loop seal clearance is single-phase vapour, and during this phase the prediction of single-phase critical flow is important in predicting inventory loss and core uncovery. Although the establishment of a vapour vent path reduces the liquid entrainment from the RCS, and hence the total mass flow, the safety injection flow remains low due to the RCS pressure, which remains high (Figure 1). As a result, the RCS inventory continues to deplete (Figure 5) throughout the boiloff phase until the accumulator check valve pressure is reached, around 2200s after the break as shown by the sudden and measurable increase in total injection flow in Figure 6. Because the accumulator injection begins the recovery, the depressurization rate is important in determining the severity in terms of core uncovery and cladding temperatures. Condensation of vapour in the proximity of the safety injection can influence this rate.

Intermediate Break LOCA (IBLOCA)

1. Blowdown/depressurization: Following an IBLOCA, the RCS depressurizes to the pressurizer low-pressure setpoint, actuating a reactor trip signal, and the control rods insert. System pressure continues to decrease as RCS inventory is lost through the break. The cold legs will reach saturation conditions, and two-phase flow at the break will lead to a reduction in the break flow rate. The break flow remains in a critical flow condition throughout this phase. As core inventory is lost, the core may rise during this phase due to decay heat generation. As in the small break LOCA, critical flow at the break is a highly-ranked phenomenon during this period.

2. Accumulator injection: Once the primary side has depressurized sufficiently, accumulator injection is initiated. The accumulator injection phase is characterized by a rapid refill of the downcomer and of the core that will typically terminate any heat-up initiated during the blowdown phase. Most important during this period of the transient is the prediction of the accumulator flowrate and the flow at the break, since the mitigation of vessel liquid inventory during this period can keep the core adequately covered.

3. Safety injection: As the accumulator empties, nitrogen will surge from the accumulator to the reactor coolant system. During this last phase, only pumped SI flow will be available to maintain core cooling. A second heat-up may occur if SI flow is not sufficient to match decay heat and the mass inventory decreases. Nitrogen in the system may affect the system response. This phase and the transient are considered complete when SI flow consistently exceeds break flow and the core is quenched. Therefore, here the prediction of critical break flow is ranked ‘H.’

As shown in Figure 7, intermediate breaks are characterized by an RCS pressure transient that does not exhibit a significant natural circulation period, but that does progress more slowly than a typical large break LOCA. Because break flow is sufficiently large, a quasi-steady natural circulation phase does not persist, and pressure falls to the accumulator check valve pressure relatively quickly in comparison with the SBLOCA transients. The 12-inch break is explored in further detail here.

As the RCS liquid becomes saturated, and flashing occurs, the transition to two-phase break flow leads to a reduction in break mass flow, shown in Figure 8. When this occurs, the depressurization rate also reduces (Figure 7). The accumulator injection rapidly refills the vessel, shown in Figure 9, as the RCS pressure is still too high to allow for appreciable safety injection. After the accumulator has emptied, approximately 160 seconds after the break in Figure 10, over 200 seconds pass in which the safety injection is less than the break flow, allowing for inventory depletion (Figure 9). Recovery occurs as safety injection exceeds break flow.

Large Break LOCA (LBLOCA)

1. Blowdown: The blowdown period extends from the initiation of the break until the primary side depressurizes sufficiently that emergency core cooling water can start to penetrate the downcomer. The flow out of the break is high, but limited by critical flow phenomena. Boiling and flashing occur in the core as the flow reverses, shutting down the fission process. The hot fuel rods quickly exceed the critical heat flux, as the core flow reverses, resulting in a sharp reduction in heat transfer to the coolant. The cladding temperature rises rapidly as the initial stored energy in the fuel pellets is transferred to the cladding. Within the next several seconds, coolant in all regions of the vessel and loops begins to flash. The break flow becomes saturated, and is substantially reduced. This reduces the depressurization rate, and may also lead to a short period of positive (upward) core flow as the intact loop pumps continue to supply coolant to the vessel. Cladding temperatures may be reduced, and some portions of the core may re-wet. Two-phase conditions in the pumps reduce their effectiveness, and the core flow again reverses. Significant core cooling occurs as the fission process shuts down, and the main heat source becomes decay heat generated in the fuel rods. Some system-level phenomena of high importance during this period include the prediction of break flow, the relative break path resistances to either the pump- or vessel-side of the break, and the prediction of flow reversal/stagnation in the core.

2. Refill: At approximately 10 to 15 seconds after the break, the RCS pressure decreases to the point where accumulators begin injecting cold water into the cold legs. As this water flows into the downcomer, it is initially swept out of the vessel and into the broken cold leg by the continuing high flow of steam from the core. Approximately 20 to 30 seconds after the break, the RCS has depressurized to a level approaching that of the containment, and refill begins. The ECC water from the accumulators and the pumped safety injection penetrates the steam upflow in the downcomer, refilling the lower plenum within a few seconds. As the coolant enters the core, the reflooding process begins. Prediction of three-dimensional effects in the downcomer is a highly-ranked phenomena, since bypass of ECC water can delay the end of refill and thus prolong cladding heat-up.

3. Reflood: The flow into the core is oscillatory, as cold water re-wets the hot fuel rods, generating steam. This steam, and the water it entrains, must pass through the vessel upper plenum, the broken loop hot leg, the steam generator, and the pump before it can be vented out the break. Entrained water that enters the steam generators is also vapourised, increasing the flow path resistance. Because of the relatively low flow during this time period, cladding temperatures continue to slowly increase until the water level in the core reaches several feet. After about 120 to 240 seconds, the cladding temperatures in the higher regions of the core begin to decrease due to heat transfer to the dispersed droplet flow. Eventually, the entire core rewets and the long-term cooling phase begins. During this period, the predictions of steam binding in the steam generators and the containment back pressure are highly important, since they influence the rate at which the core inventory can be replenished, and thus, the cladding heat-up that can occur during reflood.

Following a large break LOCA, the RCS depressurizes very quickly. In Figure 11, the RCS pressure is shown for break sizes ranging from effective break flow area (EFA) of 1.0 to 2.8, defined by the total break area divided by the cold leg area. To achieve EFA=2.8, a numerical discharge coefficient of 1.4 is applied to the vessel- and pump-side break plane to account for increased flow observed in experiments. The EFA=2.0 case, a nominal double-ended guillotine break of the cold leg (DEGCL), will be explored further here.

Figure 12 shows the vapour flow behaviour in the core during blowdown. A period of positive flow persists for approximately 10 seconds after the break. Shortly thereafter, flow reversal toward the break is apparent. By 20 seconds after the break, the vessel has depressurized and the net vapour flow is very small. It is this flow reversal and stagnation that is important in determining cladding heat-up during the blowdown period.

The accumulator check valve pressure is reached approximately 10 seconds after the break, and the accumulator begins its blowdown (Figure 13). As described by [7], although localized flooding can be described by conventional correlations (Kutateladze, and so on), the system-level phenomenon of ECC bypass is three-dimensional in nature. Adequate prediction of ECC bypass is validated in FSLOCA™ through comparison with the upper plenum test facility (UPTF) and other integral effect tests. Due to flooding phenomena in the downcomer and the resulting ECC bypass, vessel inventory continues to be lost through the break after the accumulator injection has started until the inventory reaches a minimum around 20 seconds (Figure 14) after the break, coincident with the RCS pressure reaching the containment pressure (Figure 11). The refill of the vessel continues after the end of ECC bypass, and the lower plenum liquid is replenished by the time the accumulator injection is complete (Figure 15).

The bottom-up reflood commences, driven by pumped safety injection into the cold leg, refilling the downcomer. As shown in Figure 16, the limiting elevation remains near the top of the active fuel (here, the fuel is 12 ft. tall). During reflood, as the quench front progresses upward, the upper elevations are cooled primarily by single-phase vapour and any liquid droplets entrained upward from the quench front, [8] so it is expected that higher elevations would be more limiting. A period of some 150 seconds passes between the end of refill and the time when the quench front reaches the most limiting elevation, ending the transient around 200 seconds after the break.

Full spectrum results

For the purposes of comparison, Figure 17 plots the peak cladding temperature (PCT) over the full spectrum of break sizes, shown as a fraction of the highest figure, against the effective break area. The maximum PCT is calculated to occur at A/ACL = 2.0, the double-ended guillotine break. Note that the effective break area also considers the influence of a discharge coefficient applied at the break plane; those points in Figure 17 with A/ACL greater than 2.0 are double-ended guillotine breaks with discharge coefficient greater than 1.0 on each side of the break.

Consistent with the current Westinghouse best-estimate large break LOCA analysis methodology [9], both split breaks and double-ended guillotine breaks are considered (all intermediate and small breaks are split breaks); note that the two points in Figure 17 with A/ACL = 2.0 represent one of each. When assuming nominal uncertainty parameters, the large breaks result in higher PCT than small and intermediate breaks. The limiting break size varies by plant type, depending on the relative area of the RCS pipes to the core flow area and the overall RCS liquid inventory.

A full analysis requires quantification of the uncertainties, which may vary in nature and magnitude for different break sizes. The treatment of uncertainties is addressed in [1].

Conclusions

A system-level demonstration of the recently developed FSLOCA™ methodology has been provided over the full range of postulated break sizes. For small breaks, the important phenomena of two-phase critical flow, horizontal stratification, loop seal clearance, and core mixture level have been illustrated. For intermediate breaks, the phenomena related to break flow and accumulator injection have been shown. And for large breaks, the phenomena related to blowdown flow reversal/stagnation, ECC bypass, and steam binding (entrained droplets that vaporise in steam generator tubes, impeding core reflooding) have been illustrated. It has been shown that, when modelling in a realistic fashion, nominal small and intermediate breaks tend to be less limiting than large breaks for this illustrative plant example.

 


M. A. Shockling, C. Frepoli and K. Ohkawa, Westinghouse Corp, 1000 Westinghouse Dr, Cranberry Twp., PA 16066. This article is based on a paper originally presented at the 14th International Topical Meeting on Nuclear Reactor Thermohydraulics, NURETH-14, Toronto, Ontario, Canada, 25-30 September 2011.

FULL SPECTRUM and FSLOCA are trademarks in the United States of Westinghouse Electric Company LLC, its subsidiaries and/or its affiliates.

This article was originally published in the January 2012 issue of Nuclear Engineering International magazine.


References

[1] Frepoli, C., Ohkawa, K., et al., "Realistic LOCA Evaluation Methodology Applied to the Full Spectrum of Break Sizes (FULL SPECTRUMTM LOCA Methodology)," WCAP-16996-NP, Revision 0, November 2010. (ADAMS Accession Number ML103610227)

[2] Regulatory Guide 1.203, "Transient and Accident Analysis Methods" December 2005. (ADAMS Accession Number ML053500170)

[3] Boyack, B., et al., "Quantifying Reactor Safety Margins: Application of Code Scaling, Applicability, and Uncertainty (CSAU) Evaluation Methodology to a Large-Break, Loss of Coolant Accident," NUREG/CR-5249, 1989. (ADAMS Accession Number ML030380503)

[4] Frepoli, C., "Need of a Coherent and Consistent Phenomena Identification and Ranking Table (PIRT) to Address Small, Intermediate, and Large Break LOCA in PWRs," Transactions of the American Nuclear Society, Albuquerque, NM, Nov. 12-16, 2006.

[5] Ohkawa, K., "Development of Homogeneous Non-equilibrium Relaxation Critical Flow Model with Non-condensable Gas," Paper-151, The 12th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-12), Pittsburgh, PA, USA, 2007.

[6] Lee, et al.,"Phenomenological Uncertainty During Loop Seal Steam Venting in a Small Break Cold Leg LOCA of a PWR,"ASME 83-HT-104, 1983.

[7] Glaeser, H., "Downcomer and Tie Plate Countercurrent Flow in the Upper Plenum Test Facility (UPTF)," Nuclear Engineering and Design, Vol. 133, pp. 259-283, 1992.

[8] Yadigaroglu et al., "Modeling of Reflooding," Publication Nuclear Engineering and Design, 145, 1-35, 1993.

[9] Nissley, M.E., et al., "Realistic Large Break LOCA Evaluation Methodology Using Automated Statistical Treatment of Uncertainty Method (ASTRUM)," WCAP-16009-NP-A, Revision 0, 2005. (ADAMS Accession Number ML050910157)

 

Figure 1: RCS pressure for SBLOCA by break size Figure 1: RCS pressure for SBLOCA by break size
Figure 2: RCS pressure (1) and SG secondary side pressure (2) for three-inch SBLOCA Figure 2: RCS pressure (1) and SG secondary side pressure (2) for three-inch SBLOCA
Figure 3: Break void fraction for three-inch SBLOCA Figure 3: Break void fraction for three-inch SBLOCA
Figure 4a: Loop seal clearance prediction (differential pressure) Figure 4a: Loop seal clearance prediction (differential pressure)
Figure 4b: Loop seal clearance prediction (differential pressure) Figure 4b: Loop seal clearance prediction (differential pressure)
Figure 4c: Loop seal clearance prediction (differential pressure) Figure 4c: Loop seal clearance prediction (differential pressure)
Figure 5: RCS fluid inventory for three-inch SBLOCA Figure 5: RCS fluid inventory for three-inch SBLOCA
Figure 6: Safety injection for three-inch SBLOCA Figure 6: Safety injection for three-inch SBLOCA
Figure 7: RCS pressure for IBLOCA by break size Figure 7: RCS pressure for IBLOCA by break size
Figure 8: Break flow for 12-inch IBLOCA Figure 8: Break flow for 12-inch IBLOCA
Figure 9: RCS fluid inventory for 12-inch IBLOCA Figure 9: RCS fluid inventory for 12-inch IBLOCA
Figure 10: Safety injection for 10-inch IBLOCA Figure 10: Safety injection for 10-inch IBLOCA
Figure 11: RCS pressure for LBLOCA by effective break flow area/type Figure 11: RCS pressure for LBLOCA by effective break flow area/type
Figure 12: Vapour mass flow rate in core for DEGCL Figure 12: Vapour mass flow rate in core for DEGCL
Figure 13: Accumulator flow in DEGCL Figure 13: Accumulator flow in DEGCL
Figure 14: RCS fluid inventory in DEGCL Figure 14: RCS fluid inventory in DEGCL
Figure 15: Lower plenum level for DEGCL Figure 15: Lower plenum level for DEGCL
Figure 16: Peak cladding temperature location for DEGCL Figure 16: Peak cladding temperature location for DEGCL
Figure 17: Peak cladding temperature against effective break area Figure 17: Peak cladding temperature against effective break area


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