To design a scale model of a PWR passive residual heat removal system that preserves and controls the two-phase flow instability, defined as unstable oscillations of the condensate water level at the saturated steam/water interface in the vertical condensate pipe column, non-dimensional (Pi) groups were derived using the top-down (macroscopic) modeling approach known as the Buckingham Pi Theorem. Subsequently, the scaling ratios and scaling laws for the two-phase flow instability-related parameters of the system design-expressed in terms of the ratios of pipe length and diameter between the scale model and the full-size system-were derived based on the relationships between the Pi groups. The scaling ratios obtained for the parameters such as length, diameter, area, volume, time, oscillation frequency, mass flow rate, heat input, and pressure drop were compared with those derived from bottom-up (microscopic/fine structure) modeling approaches, including the three-level and hierarchical two-tiered scaling methods. As a result, the findings of this study align with those obtained using either the three-level or hierarchical two-tiered scaling method, except for the heat input (power) scaling ratio and the power-volume scaling ratio. From a dimensional similarity perspective, the present method appears to yield physically consistent values for the heat input and power-volume scaling ratios, which are defined as the product of the length scaling ratio and the corresponding scaling ratio derived from either the three-level or hierarchical two-tiered scaling method. Consequently, this study makes a significant contribution to engineering literature by demonstrating that the Buckingham Pi Theorem can establish scaling laws for designing a scale model to predict and interpret full-scale system behavior without requiring a comprehensive understanding of transient two-phase flow phenomena, unlike bottom-up approaches that necessitate detailed knowledge of the underlying phenomena.

A simplified analytical model is developed for estimating the initial waterhammer pressure and force on a circular tube when a plane decompression wave, parallel to its axis, passes over it. The simplified analysis superimposes the solutions for a plane pressure wave traveling at sound speed in the surrounding water, and two-dimensional solution to the wave equation in cylindrical coordinates, with a nonflow boundary condition across the tube boundary at a fixed radius. The analytical method is compared to the computational fluid dynamics (CFD) approach by applying to predict the initial waterhammer pressure and force on the closest tube to the feedwater nozzle of a geometrically simplified nuclear steam generator (SG) analysis model, caused by a feedwater pipe break (FWPB). As the result, it is found that the simplified analytical model, while not matching results of the CFD calculations with precise accuracy, does confirm the nature of the waterhammer impact pressure loads on the SG tubes.

For the structural integrity evaluation of pressurized water reactor (PWR) steam generator (SG) tubes subjected to transient hydraulic loading, determination of the tube-to-tube gap velocity and static pressure distributions along the tubes is prerequisite. This paper addresses both computational fluid dynamics (CFD) and analytical approaches for predicting the tube-to-tube gap velocity and static pressure distributions during blowdown following a feedwater line break (FWLB) accident at a PWR SG. First of all, a comparative study on CFD calculations of the transient velocity and pressure distributions in the SG secondary sides for two different models having 30 or no tubes is performed. The result shows that the velocities of sub-cooled water flowing between any adjacent two tubes of a tubed SG model during blowdown can be roughly estimated by applying the specified SG secondary side porosity to those of the no-tubed SG model. Secondly, simplified analytical approximate solutions for the steady two-dimensional SG secondary flow velocity and pressure distributions under a given discharge flowrate are derived using a line sink model. The simplified analytical solutions are validated by comparing them to the CFD calculations.

This paper presents a numerical prediction of the transient hydraulic loads acting on the tubes and external supports of a pressurized water reactor (PWR) steam generator (SG) during blowdown following a sudden feedwater line break (FWLB). A simplified SG model was used to easily demonstrate the prediction. The blowdown discharge flow was treated as a flashing flow to realistically simulate the transient flow fields inside the SG and the connected broken feedwater pipe. The effects of the SG initial pressure or the broken feedwater pipe length on the intensities or magnitudes of transient hydraulic loads were investigated. Then predictions of the decompression pressure wave-induced impulsive pressure differential loads on SG tubes and the transient blowdown loads on SG external supports were demonstrated and the general aspects of transient responses of such transient hydraulic loads to the FWLB were discussed.

This paper investigates the effects of steam generator initial pressure and length of a broken feedwater pipe on the transient hydraulic loads on the pressurized water reactor (PWR) steam generator (SG) tubes and supports during blowdown following a sudden feedwater line break (FWLB). To do this, the transient flow fields inside the SG and the connected broken feedwater pipe are calculated by realistically treating the discharge flow as the sub-cooled water flashing flow. Then, the calculated transient flow field data are used to predict the transient hydraulic loads on the PWR SG tubes and supports for some specified cases where the SG initial pressure or the broken feedwater pipe length are different from each other.

A computational fluid dynamics (CFD) analysis was performed to predict the transient hydrodynamic loads exerted on the steam generator tubes and the thrust forces on the broken pipe (which is equal to the impingement forces on target structures in the expanding fluid jet path) during a main feed water line break (FWLB) accident at a pressurized water reactor (PWR) power plant. To address a possible severe case of the transient hydrodynamic loads, the break was assumed to occur at the circumferential weld line between the feed water nozzle and the main feed water pipe so that the compressed sub-cooled water would be discharged through the short broken pipe. Thus, a sub-cooled liquid flashing flow through the broken short feed pipe was simulated numerically. Typical results of the prediction were illustrated and discussed. In addition, the present simulation in terms of the transient mass flow rates during the blowdown following the MFLB was compared to other previous calculations. Based on the discussions, the present simulation is considered to be physically plausible and more realistic than other previous predictions.

A computational fluid dynamics (CFD) analysis was performed to investigate the hydraulic response of the flow field inside the pressurized water reactor (PWR) steam generator (SG) secondary side and the connected part of main feed water pipe to an abrupt main feed water line break (FWLB) accident. To realistically analyze the transient flow field situation, the flow field was assumed to be occupied initially by highly compressed subcooled water except that the upper part of the SG secondary side where steam occupied as in the practical case and the break was assumed to occur at the circumferential weld line between the feed water nozzle and the main feed water pipe. This would result in a subcooled water flashing flow from the SG through the short-broken pipe end to the surrounding atmosphere, which was numerically simulated in this study. Typical results of the prediction in terms of the fluid transient velocity and pressure were illustrated and discussed. To examine the physical validity of the present numerical simulation of the subcooled water flashing flow, the transient mass flow rates predicted in this study were compared with the other previous numerical predictions based on the subcooled water nonflashing (no phase change) flow or saturated water flashing flow assumptions and the prediction by a simple analysis method.

Transient fluid velocity and pressure fields in a pressurized water reactor (PWR) steam generator (SG) secondary side during the blowdown period of a feedwater line break (FWLB) accident were numerically simulated employing the saturated water flashing model. This model is based on the assumption that compressed water in the SG is saturated at the beginning and decompresses into the two-phase region where saturated vapor forms, creating a mixture of steam bubbles in water by bulk boiling. The numerical calculations were performed for two cases of which the outflow boundary conditions are different from each other; one is specified as the direct blowdown discharge to the atmosphere and the other is specified as the blowdown discharge to an extended calculation domain with atmospheric pressure on its boundary. The present simulation results obtained using the two different outflow boundary conditions were discussed through a comparison with the predictions using a simple non-flashing model neglecting the effects of phase change. In addition, the applicability of each of the non-flashing water discharge and saturated water flashing models for the confirmatory assessments of new SG designs was examined.

Transient fluid velocity and pressure fields in a pressurized water reactor (PWR) steam generator (SG) secondary side during the blowdown period of a feedwater line break (FWLB) accident were numerically simulated employing the saturated liquid flashing model. This model is based on the assumption that compressed water in the SG is saturated at the beginning and decompresses into the two-phase region where saturated vapor forms, creating a mixture of steam bubbles in liquid by bulk boiling. The numerical calculations were performed for two cases where the outflow boundary condition is different from each other; one is specified as the direct blowdown discharge to atmospheric pressure and the other is specified as the blowdown discharge to an extended calculation domain with atmospheric pressure on its boundary. To effectively simulate the saturated water flashing from the SG following the FWLB accident, the physical SG model was simplified as a vertical once-through SG to which a feedwater pipe is attached. However, the physical geometry of the analysis model was modeled as realistically as possible in terms of the SG tube bundle height, the SG inner diameter and porosity, the inner diameter and length of broken feedwater pipe part, etc. It was considered that the SG shell-side and the attached feedwater pipe were initially filled with high pressure saturated water. The pressure in the steam space was 7.5 MPa. For the calculation of the two-phase flow during high pressure saturated water flashing from the SG through the broken feedwater pipe, the inhomogeneous two-fluid model was used. The present simulation results were discussed through a comparison with the predictions using a simple non-flashing model neglecting the effects of phase change. Based on the comparative discussions, the applicability of each of the non-flashing liquid discharge and saturated liquid flashing discharge models to the confirmatory safety evaluations of new SG designs was examined.

In this study, a computational fluid dynamics (CFD) analysis of the transient flow field inside the secondary side of a nuclear reactor steam generator (SG) during blowdown following a feedwater line break (FWLB) accident is performed to evaluate the transient hydraulic loading (pressure) on the SG internals and tubes. The nonflashing liquid flow is assumed for a conservative prediction of the transient blowdown loading. The CFD analysis results are illustrated in terms of the transient velocity and pressure disturbances at some selected monitoring points inside the SG secondary side and compared with those predictions obtained from the existing simple analytical model to examine the physical validity of the CFD analysis model. As a result, the existing simple analytical model cannot yield the transient velocity and pressure disturbances and results in underestimation during blowdown as compared to the CFD calculations. Based on the present CFD analysis results, it is seen that an FWLB may result in excessive disastrous transient hydraulic loading on the SG internal structures and tubes near the feedwater inlet nozzle due to the significant pressure changes (pressure wave with very high amplitude) and abruptly increased velocity of water near the feedwater nozzle.

This paper presents an evaluation of the applicability of a numerical analysis model to the transient thermal-hydraulic response of steam generator (SG) secondary side to blowdown following a steam line break (SLB) at a pressurized water reactor (PWR). To do this, the numerical analysis model was applied to simulate the same blowdown situation as in an available experiment which was conducted for a simplified SG blowdown model, and the numerical results were compared with the measurements. As a result, both are in reasonably good agreement with each other. Consequently, the present numerical analysis model is evaluated to have the applicability for numerical simulations of the transient phase change heat transfer and flow situations in PWR SGs during blowdown following a SLB.

A numerical analysis has been performed to simulate the transient thermal-hydraulic response to a main steam line break (MSLB) for the secondary side of a steam generator (SG) model equipped with a venturi-type SG outlet flow restrictor at a pressurized water reactor (PWR) plant. To investigate the effects of the flow restrictor on the thermal-hydraulic response of SG to the MSLB, numerical calculation results for the SG model equipped with the flow restrictor are compared to those obtained for an SG model without the restrictor. Both analysis models contain internal structures. The present computational fluid dynamics (CFD) model has been examined by comparing to a simple analytical model. It is confirmed from the comparison that the CFD model simulates the transient response of the SG secondary to the MSLB physically plausibly and minutely. Based on the CFD analysis results for both cases with or without the restrictor, it is seen that the intensities of the steam velocity and dynamic pressure are considerably attenuated in the SG model equipped with the restrictor comparing to the case in the SG model without the restrictor.

This paper presents a multi-dimensional numerical analysis of the transient thermal-hydraulic response of a steam generator secondary side to a double-ended guillotine break of the main steam line attached to the steam generator at a pressurized water reactor plant. A simplified analysis model is designed to include both the steam generator upper space where steam occupies and a part of the main steam line between the steam generator outlet nozzle and the pipe break location upstream of the main steam isolation valve. The transient steam flow through the analysis model is simulated using the shear stress transport turbulence model. The steam is treated as a real gas. To model the steam generation by heat transfer from the primary coolant to the secondary side coolant for a short period during the blow down process following the main steam line break accident, a constant amount of steam is assumed to be generated from the bottom of the steam generator upper space part. Using the numerical approach mentioned above, calculations have been performed for the analysis model having the same physical dimensions of the main steam line pipe and initial operational conditions as those for an actual operating plant. The calculation results have been discussed in detail to investigate their physical meanings and validity. The results demonstrate that the present CFD model is applicable for simulating the transient thermal-hydraulic responses in the event of the MSLB accident including the blowdown-induced dynamic pressure disturbance in the SG. In addition, it has been found that the dynamic hydraulic loads acting on the SG tubes can be increased by 2 to 8 times those loads during the normal reactor operation. This implies the need to re-assess the potential for single or multiple SG tube ruptures due to fluidelastic instability for ensuring the reactor safety.

A PWR incorporates a passive auxiliary feedwater system (PAFS), a closed natural circulation loop which is aligned to feed condensed water to its corresponding steam generator (SG). During its operation, saturated steam in the SG secondary side moves up due to buoyancy force and passes through a steam line, and then flows into a tube-tank type passive condensation heat exchanger where steam is condensed inside the tubes while the tube outer surfaces are cooled by the pool water. The condensate water is passively fed into the SG economizer by gravity. Because a natural circulation loop is susceptible to two-phase flow instability, it is requisite to confirm the system is designed adequately to avoid the potential challenges to its operational safety due to the instability.This paper presents an analytical approach for assessing if the PAYS has possible thermal and fluid mechanical characteristics which could lead to an undesirable unstable or oscillating condensate water level in the vertical pipe section. Both steady and unsteady analytical solutions for a simplified natural circulation loop model of the PAFS were derived in terms of the condensate water level and velocity in the vertical pipe section. From the solutions, the criteria for determining a potential for two-phase instability in the system were obtained.

A pressurized water reactor (PWR) incorporates a passive auxiliary feedwater system (PAFS), a closed natural circulation loop which is aligned to feed condensed water to its corresponding steam generator (SG). During its operation, saturated steam in the SG secondary side moves up due to buoyancy force and passes through a steam line, and then flows into a tube-tank type passive condensation heat exchanger (PCHX) where steam is condensed inside the tubes while the tube outer surfaces are cooled by the pool water. The condensate water is passively fed into the bottom of the SG secondary side by gravity. Because a natural circulation loop is susceptible to two-phase flow instability, it is requisite to confirm the system is designed adequately to avoid the potential challenges to its operational safety due to the instability. This paper presents an analytical approach for assessing if the PAFS has possible thermal and fluid mechanical characteristics which could lead to an undesirable unstable or oscillating condensate water level in the vertical pipe section. Both steady and unsteady analytical solutions for a simplified natural circulation loop model of the PAFS were derived in terms of the condensate water level and velocity in the vertical pipe section. From the solutions, the criteria for determining a potential for flow instability in the system were obtained.

A PWR design incorporates a passive auxiliary feedwater system equipped with one passive condensation heat exchanger (PCHX) which consists of inclined V-shaped tube bundles submerged in a water pool of which the top is open to the atmosphere. During the PCHX operation, saturated steam flows into the PCHX where steam is condensed inside of the tubes by cooling the outer side with the pool water. Then, the condensate flows out passively by gravity. Because the thermal-hydraulic characteristics in the PCHX determine the condensation mass rate and the possibility of thermal stratification-induced fatigue of the pool tank wall, system instability and waterhammer, it is important to understand the phase change flow in the PCHX. In this paper, the complex phase change heat transfer and multi-phase flow in a PCHX tube model were numerically simulated. The single fluid multi-component flow model with the equilibrium phase change model was employed for the condensation phase change flow inside the tube and the two-fluid model with the wall boiling model and the equilibrium phase change model was used for the boiling-induced natural convection outside the tube in the pool. Based on the present numerical simulation, the characteristics of the heat transfer and flow in the PCHX are discussed and illustrated for some typical results.

Temperature of pressurized water reactor (PWR) core is a key parameter used widely for judging the initiation of emergency operating procedures and severe accident management. Since direct measurement of the fuel cladding surface temperature using thermocouples is not practicable currently, the coolant temperature at the core exit locations is monitored instead. Several experimental researches showed that the CET rise during a loss of coolant accident (LOCA) and its magnitudes were always lower than the actual fuel rod cladding temperature at the same time. In this regard, a theoretical analysis of the transient heat transfer of coolant flow in a PWR core is needed to confirm the findings from the previous experimental works. This paper addresses numerical simulation of the transient boiling-induced multiphase flow through a simplified PWR core model during a LOCA by a commercial computational fluid dynamics (CFD) code. The calculated results are discussed to understand the transient heat transfer mechanism in the core and to provide useful technical information for reactor design and operation.