10.2 Pressurized water reactors

Pressurized water reactors (PWRs) are the most common nuclear reactors, using high-pressure water as coolant and moderator. They operate with separate primary and secondary coolant loops, allowing efficient heat transfer from the reactor core to generate electricity.

PWRs face unique thermal hydraulic challenges, including subcooled nucleate boiling and critical heat flux phenomena. Understanding these processes is crucial for safe operation, involving complex multiphase flow modeling and addressing operational issues like crud deposition and reactor vessel embrittlement.

Pressurized water reactor fundamentals

• Pressurized water reactors (PWRs) are the most common type of nuclear reactor, using pressurized water as coolant and moderator
• PWRs operate at high pressure (around 155 bar) to keep the water in a liquid state at high temperatures, allowing for efficient heat transfer from the reactor core to the steam generators
• The reactor core contains the nuclear fuel assemblies, control rods, and various instrumentation to monitor and control the fission reaction

Primary vs secondary coolant loops

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• PWRs utilize two separate coolant loops: the primary loop and the secondary loop
• The primary loop circulates pressurized water through the reactor core, absorbing heat generated by nuclear fission
  • This heated water is then pumped to the steam generators, where it transfers its heat to the secondary loop
• The secondary loop contains water that is converted to steam by the heat from the primary loop
  • The steam drives the turbine-generator set to produce electricity
  • The steam is then condensed back into water and returned to the steam generators, completing the secondary loop

Pressure vessel design considerations

• The reactor pressure vessel (RPV) is a crucial component that houses the reactor core and contains the primary coolant
• RPV design must account for high pressure, temperature, and radiation levels to ensure safe operation
• Key design considerations include:
  • Material selection (typically low-alloy steel with stainless steel cladding)
  • Wall thickness to withstand internal pressure
  • Nozzle placement for coolant inlet and outlet
  • Provisions for control rod drive mechanisms and instrumentation penetrations
• Regular inspections and maintenance are essential to monitor RPV integrity over the reactor's lifetime

Core heat transfer mechanisms

• Heat transfer in the reactor core occurs through several mechanisms:
  • Conduction: heat transfer through the fuel pellets and cladding
  • Convection: heat transfer from the fuel rods to the surrounding coolant
  • Radiation: heat transfer from the fuel rods to the coolant and other core components
• The primary mode of heat transfer in the core is convection, with the coolant flow removing heat from the fuel rods
• Proper heat transfer is crucial to maintain fuel integrity and prevent overheating

Subcooled nucleate boiling

• Subcooled nucleate boiling occurs when the coolant temperature is below the saturation temperature, but local heating causes the formation of steam bubbles on the fuel rod surface
• This phenomenon enhances heat transfer by increasing the surface area for convection and agitating the boundary layer
• Subcooled nucleate boiling is a desirable condition in PWRs, as it promotes efficient heat removal from the fuel rods
• However, excessive boiling can lead to reduced heat transfer and potential fuel damage, so it must be carefully monitored and controlled

Thermal hydraulics of PWRs

• Thermal hydraulics is the study of fluid flow and heat transfer in the reactor system, particularly in the core and primary coolant loop
• Understanding thermal hydraulics is essential for designing and operating PWRs safely and efficiently
• Key aspects of PWR thermal hydraulics include coolant flow regimes, heat transfer correlations, critical heat flux, and departure from nucleate boiling

Coolant flow regimes

• Coolant flow in PWRs can exhibit different flow regimes depending on the local conditions (e.g., temperature, pressure, and heat flux)
• Common flow regimes include:
  • Single-phase liquid flow: occurs in the majority of the primary loop, where the coolant remains in a liquid state
  • Bubbly flow: characterized by the presence of discrete steam bubbles in a continuous liquid phase, typically observed in subcooled nucleate boiling
  • Slug flow: occurs when steam bubbles coalesce into larger bubbles or slugs, intermittently occupying the flow channel
  • Annular flow: characterized by a continuous steam phase in the center of the flow channel, with a liquid film along the walls
• Identifying and predicting flow regimes is crucial for accurate modeling of heat transfer and fluid dynamics in the reactor core

Heat transfer correlations

• Heat transfer correlations are empirical relationships used to predict heat transfer coefficients and other parameters based on fluid properties, flow conditions, and geometry
• These correlations are essential for designing and analyzing PWR components, such as fuel assemblies and steam generators
• Examples of commonly used heat transfer correlations in PWRs include:
  • Dittus-Boelter correlation: predicts the convective heat transfer coefficient for single-phase turbulent flow in pipes
  • Chen correlation: estimates the heat transfer coefficient for saturated nucleate boiling, accounting for both convective and boiling contributions
  • Thom correlation: predicts the wall superheat required for the onset of nucleate boiling
• Selecting appropriate correlations and validating them against experimental data is crucial for accurate thermal hydraulic modeling

Critical heat flux phenomena

• Critical heat flux (CHF) refers to the maximum heat flux that a surface can sustain before the onset of a rapid decrease in heat transfer efficiency
• In PWRs, CHF is a crucial safety limit, as exceeding it can lead to a sudden reduction in heat removal from the fuel rods, potentially causing fuel damage
• CHF can occur due to two main mechanisms:
  • Departure from nucleate boiling (DNB): when the steam bubbles formed during nucleate boiling coalesce and form a vapor film, insulating the surface from the liquid coolant
  • Dryout: when the liquid film in annular flow is depleted, exposing the surface to the steam phase
• Predicting and avoiding CHF is a primary concern in PWR design and operation, as it ensures the fuel remains adequately cooled

Departure from nucleate boiling

• Departure from nucleate boiling (DNB) is a specific type of critical heat flux that occurs when steam bubbles formed during nucleate boiling coalesce and form a vapor film on the fuel rod surface
• The vapor film acts as an insulating layer, reducing heat transfer from the fuel rod to the coolant and potentially leading to fuel damage
• The point at which DNB occurs is characterized by the departure from nucleate boiling ratio (DNBR), which is the ratio of the predicted CHF to the actual local heat flux
  • Maintaining a DNBR above 1 ensures that the fuel rods are adequately cooled and prevents DNB
• Accurate prediction of DNB is essential for setting operational limits and ensuring reactor safety

Safety considerations in PWRs

• Nuclear reactor safety is of paramount importance, and PWRs incorporate various systems and features to prevent accidents and mitigate their consequences
• Key safety considerations in PWRs include reactivity control systems, emergency core cooling systems, containment design, and severe accident mitigation strategies

Reactivity control systems

• Reactivity control systems are designed to regulate the fission reaction rate in the reactor core and ensure safe operation
• The primary reactivity control system in PWRs is the control rod drive mechanism (CRDM), which allows the insertion or withdrawal of control rods containing neutron-absorbing materials (such as boron carbide or silver-indium-cadmium alloys)
  • Inserting control rods reduces reactivity and slows down the fission reaction, while withdrawing them increases reactivity
• Other reactivity control methods include:
  • Burnable poison rods: contain neutron-absorbing materials that deplete over time, helping to manage long-term reactivity changes
  • Soluble boron control: boron is added to the primary coolant to absorb neutrons and control reactivity
• Redundant and diverse reactivity control systems are employed to ensure reliable shutdown capability

Emergency core cooling systems

• Emergency core cooling systems (ECCS) are designed to provide cooling to the reactor core in the event of a loss-of-coolant accident (LOCA)
• ECCS components include:
  • High-pressure injection system: rapidly injects borated water into the reactor vessel to maintain core cooling and reactivity control
  • Low-pressure injection system: provides long-term cooling after the reactor pressure has decreased
  • Accumulators: passive devices that inject borated water into the reactor vessel when the pressure drops below a certain threshold
• ECCS design ensures that the core remains covered and cooled even in the event of a large-break LOCA, preventing fuel damage and radioactive release

Containment design features

• The containment building is a robust structure that surrounds the reactor vessel and primary coolant system, serving as the final barrier against the release of radioactive materials to the environment
• PWR containment designs typically include:
  • Steel liner: a thick steel shell that provides a leak-tight barrier
  • Concrete walls: reinforced concrete walls that provide structural strength and radiation shielding
  • Pressure suppression systems: devices (such as ice condensers or water pools) that reduce the pressure and temperature inside the containment during an accident
• Containment buildings are designed to withstand extreme conditions, such as high pressure, temperature, and seismic events

Severe accident mitigation strategies

• Severe accident mitigation strategies are designed to manage and mitigate the consequences of beyond-design-basis accidents, such as core melt scenarios
• Examples of severe accident mitigation features in PWRs include:
  • Core catcher: a structure below the reactor vessel designed to catch and retain molten core material in the event of a vessel failure
  • Hydrogen recombiners: devices that convert hydrogen gas (generated during a severe accident) back into water, preventing explosive concentrations
  • Filtered venting systems: allow for the controlled release of pressure from the containment while filtering out radioactive particles
• These strategies aim to minimize the impact of severe accidents and prevent the release of radioactive materials to the environment

PWR multiphase flow modeling

• Multiphase flow modeling is crucial for accurately predicting the thermal hydraulic behavior of PWRs, particularly in the reactor core where both liquid water and steam are present
• Key aspects of PWR multiphase flow modeling include two-phase flow patterns, drift flux vs. two-fluid models, constitutive relations for closure, and computational fluid dynamics approaches

Two-phase flow patterns

• Two-phase flow patterns describe the spatial distribution of liquid and vapor phases in a flow channel
• Common two-phase flow patterns in PWRs include:
  • Bubbly flow: discrete vapor bubbles dispersed in a continuous liquid phase
  • Slug flow: larger vapor bubbles or slugs that intermittently occupy the flow channel
  • Churn flow: a chaotic flow regime with irregular vapor structures and oscillating liquid-vapor interfaces
  • Annular flow: a continuous vapor core surrounded by a liquid film along the channel walls
• Accurately predicting flow pattern transitions is essential for modeling heat transfer and fluid dynamics in the reactor core

Drift flux vs two-fluid models

• Two main approaches for modeling two-phase flows in PWRs are the drift flux model and the two-fluid model
• The drift flux model treats the two-phase mixture as a single fluid with average properties, while accounting for the relative motion between the phases using a drift flux term
  • Drift flux models are simpler and computationally less expensive, making them suitable for many engineering applications
• The two-fluid model treats the liquid and vapor phases as separate fluids with their own conservation equations for mass, momentum, and energy
  • Two-fluid models provide a more detailed description of the two-phase flow but require additional closure relations and are computationally more demanding
• The choice between drift flux and two-fluid models depends on the desired level of accuracy, computational resources, and specific application

Constitutive relations for closure

• Constitutive relations are empirical or semi-empirical equations that provide closure for the governing equations in two-phase flow models
• These relations describe various interfacial and wall transfer phenomena, such as:
  • Interfacial drag: the force exerted by one phase on the other due to relative motion
  • Interfacial heat and mass transfer: the exchange of energy and mass between the phases due to temperature and concentration gradients
  • Wall friction: the shear stress exerted by the fluid on the channel walls
  • Wall heat transfer: the heat exchange between the fluid and the channel walls
• Accurate constitutive relations are essential for capturing the complex interactions between the phases and the flow channel, and they are often derived from experimental data or high-fidelity simulations

Computational fluid dynamics approaches

• Computational fluid dynamics (CFD) is a powerful tool for simulating multiphase flows in PWRs, providing detailed information on flow patterns, temperature distributions, and other relevant parameters
• CFD approaches for multiphase flows can be classified into two main categories:
  • Eulerian-Eulerian methods: treat both phases as interpenetrating continua, solving separate conservation equations for each phase (e.g., two-fluid models)
  • Eulerian-Lagrangian methods: treat the continuous phase (usually liquid) as a Eulerian field, while the dispersed phase (usually vapor bubbles) is tracked individually using Lagrangian particles
• Advanced CFD techniques, such as interface-tracking methods (e.g., Volume of Fluid or Level Set), can provide high-resolution simulations of two-phase flows, but they are computationally expensive and often limited to small-scale applications
• The choice of CFD approach depends on the desired level of detail, computational resources, and the specific phenomena of interest

PWR operational challenges

• PWR operation can be affected by various challenges that impact reactor performance, safety, and component integrity
• Key operational challenges in PWRs include crud deposition and boiling, axial offset anomaly, pellet-cladding interaction, and reactor vessel embrittlement

Crud deposition and boiling

• Crud is a deposit that forms on the surface of fuel rods and other primary system components, consisting of corrosion products, coolant impurities, and radioactive materials
• Crud deposition can lead to several issues:
  • Reduced heat transfer efficiency: crud acts as an insulating layer, impeding heat transfer from the fuel rods to the coolant
  • Localized corrosion: crud deposits can create local hotspots and accelerate corrosion of the fuel cladding
  • Crud-induced power shift (CIPS): uneven crud distribution can cause power imbalances and affect reactor control
• Crud deposition can also lead to crud-induced localized boiling (CILB), where steam bubbles form underneath the crud layer, further reducing heat transfer and potentially causing fuel damage
• Mitigating crud deposition involves maintaining high coolant purity, optimizing pH control, and using advanced fuel cladding materials

Axial offset anomaly

• Axial offset anomaly (AOA) is a phenomenon where the axial power distribution in the reactor core deviates from the predicted shape, typically characterized by a shift in power towards the bottom of the core
• AOA is often associated with crud deposition and boron accumulation in the upper regions of the core, which can lead to reduced power output and operational challenges
• Factors contributing to AOA include:
  • Coolant chemistry: suboptimal pH or elevated levels of impurities can promote crud formation
  • Core design: certain fuel assembly designs or loading patterns may be more susceptible to AOA
  • Operational history: long cycles or high-power operation can increase the risk of AOA
• Mitigating AOA involves careful control of coolant chemistry, optimizing core design and fuel management, and monitoring core power distribution using advanced instrumentation

Pellet-cladding interaction

• Pellet-cladding interaction (PCI) refers to the mechanical and chemical interactions between the fuel pellets and the cladding tube that surrounds them
• PCI can lead to several issues:
  • Cladding stress and strain: as fuel pellets expand due to thermal expansion and fission gas release, they can exert stress on the cladding, potentially causing deformation or failure
  • Stress corrosion cracking (SCC): the combination of mechanical stress and corrosive fission products (such as iodine) can cause cracks in the cladding
  • Fuel rod failure: severe PCI can lead to cladding breach and the release of radioactive materials into the primary coolant
• Mitigating PCI involves using advanced fuel designs (such as doped pellets or coated cladding), optimizing power ramp rates, and maintaining a robust fuel performance monitoring program

Reactor vessel embrittlement

• Reactor vessel embrittlement is the gradual loss of ductility and toughness in the reactor pressure vessel (RPV) steel due to long-term exposure to high temperatures and neutron irradiation
• Embrittlement can increase the risk of RPV failure, particularly during transient events (such as pressurized thermal shock) where the vessel is subjected to rapid cooling and high stress
• Factors affecting RPV embrittlement include:
  • Material composition: the presence of certain alloying elements (such as copper and nickel) can accelerate embrittlement
  • Neutron fluence: higher neutron exposure leads to more severe embrittlement
  • Operating temperature: higher temperatures can promote embrittlement by enhancing the diffusion of alloying elements
• Mitigating RPV embrittlement involves using low-copper steel, optimizing operating conditions to minimize neutron exposure, and conducting regular surveillance tests to monitor the vessel's mechanical properties
• In some cases, RPV annealing (heat treatment) may be used to restore some of the lost ductility and toughness