Reactor Engineering Essentials

Cheatsheet Content

1. Reactor Types & Classifications Based on Moderator: D$_2$O: ZERLINA, KAMINI, DHRUVA (PHWR) H$_2$O: APSARA (swimming pool type) Graphite: GCR (Gas Cooled Reactor) Based on Coolant: H$_2$O: APSARA, PWR, BWR Liquid Na (Sodium): KAMINI, Fast Reactors (e.g., FBTR, PFBR) Gas Cooled: GCR, AGCR (CO$_2$), HTGR (He) Key Reactor Types: PHWR (Pressurized Heavy Water Reactor) SGHWR (Steam Generating Heavy Water Reactor) LWR (Light Water Reactor): PWR (Pressurized Water Reactor), BWR (Boiling Water Reactor) GCR (Gas Cooled Reactor) Fast Reactors: FBR (Fast Breeder Reactor), FBTR (Fast Breeder Test Reactor), PFBR (Prototype Fast Breeder Reactor) SMR (Small Modular Reactor): MSBR (Molten Salt Breeder Reactor) Indian Reactors: APSARA: Swimming pool type, 1 MWT (old), upgraded to 2 MWT. Fuel: Enriched U. DHRUVA: High flux research reactor, 100 MWT. Fuel: Natural Uranium Metal. D$_2$O moderator/coolant. KAMINI: Liquid Na coolant, U-233 fuel. PHWRs (e.g., 220 MWe PHWR, 540 MWe PHWR): Natural Uranium fuel. CIRUS: 40 MWT, Natural Uranium Metal fuel. 2. Light Water Reactors (LWR) - PWR & BWR Require enriched U (~3-5% U-235). PWR (Pressurized Water Reactor): Primary Heat Transport (PHT) loop is highly pressurized (~15.5 MPa) to prevent boiling of coolant (H$_2$O). Secondary loop generates steam in a Steam Generator (SG) for the turbine. Efficiency: ~30-35%. Control rods inserted from the top. High power density (~100 MW/t). Avg. Burnup: ~33,000 MWd/t. Coolant Outlet Temp: $320^\circ$C. BWR (Boiling Water Reactor): Boiling occurs directly in the core, steam goes to the turbine. No separate heat exchanger/steam generator. Control rods inserted from the bottom. Lower pressure than PWR (~7 MPa). Lower power density than PWR (~50 MW/t) because water boils. Avg. Burnup: ~33,000 MWd/t. Coolant Outlet Temp: $285^\circ$C. Increased corrosion on clad and fuel due to boiling coolant/moderator. 3. Pressurized Heavy Water Reactors (PHWR) Heavy water (D$_2$O) as moderator and coolant. Uses Natural Uranium fuel. Moderator is cooled in a separate circuit to maintain low temperature. Low moderator temperature $\rightarrow$ lower energy neutrons (thermalized) $\rightarrow$ higher cross-section for fission. Coolant pressure: ~10 MPa. Power Density: ~10 MW/t (much lower than LWRs). Avg. Burnup: ~7,500 MWd/t. Coolant Outlet Temp: $300^\circ$C. Lower power density requires higher Vm/Vf (moderator-to-fuel volume ratio). Online refueling is a key feature. 4. Sodium Cooled Liquid Metal Fast Reactors (Fast Reactors) Fast Neutron Spectrum (no moderator). Coolant: Liquid Sodium (Na). Examples: FBTR (Fast Breeder Test Reactor), PFBR (Prototype Fast Breeder Reactor). Designed for breeding new fuel (e.g., Pu-239 from U-238). High power density. 5. Gas Cooled Reactors (GCR, AGCR, HTGR) Advanced Gas Cooled Reactor (AGCR): Coolant: CO$_2$. Moderator: Graphite. Pressure: 16.5 MPa. Power Density: 11 MW/t. Avg. Burnup: 29,000 MWd/t. Enrichment: 2-3%. Coolant Outlet Temp: $650^\circ$C. High Temperature Gas Cooled Reactor (HTGR): Coolant: Helium (He). Moderator: Graphite. Pressure: 7 MPa. Power Density: 7 MW/t. Avg. Burnup: 29,000 MWd/t. Enrichment: 2-3%. Coolant Outlet Temp: $750^\circ$C (highest of listed types). 6. Auxiliary Systems to Primary Heat Transport System Pressurizer System (PWR): Maintains system pressure within limits during transients. Accommodates coolant volume changes due to temperature variations. Steam Pulsing System: Manages steam transients. Heats Feed & Bleed System (e.g., 220 MWe PHWR): Maintains primary coolant chemistry (very low conductivity). Removes radioactive particles using ion exchange. Provides lost head. Reduces tritium build-up in D$_2$O. Make-up Water System: Replenishes coolant lost during normal operation. ECCS (Emergency Core Cooling System): Activated during a LOCA (Loss of Coolant Accident). Injects coolant into the core to prevent fuel damage and melt. ARS (Reactor Regulating System): Controls reactor power during normal operation and transients. Responds to set-point changes. RPS (Reactor Protection System): Detects abnormal conditions and initiates rapid reactor shutdown (scram) to prevent damage. SDCS (Shut-Down Cooling System): Removes decay heat from the core after reactor shutdown. Maintains the reactor in a safe, cold state. Other auxiliary systems: Reheater, Cooling tower (for normal operation and heat rejection). 7. Comparative Parameters of Reactor Types Parameter PWR BWR PHWR AGCR HTGR Pressure (MPa) 15.5 7 10 16.5 7 Power Density (MW/t) 100 50 10 11 7 Avg. Burnup (MWd/t) 33,000 33,000 7,500 29,000 29,000 Enrichment 3-5% 3-5% Natural U 2-3% 2-3% Coolant H$_2$O H$_2$O D$_2$O CO$_2$ He Moderator H$_2$O H$_2$O D$_2$O Graphite Graphite Coolant Outlet Temp. $320^\circ$C $285^\circ$C $300^\circ$C $650^\circ$C $750^\circ$C 8. Fuel Pin Design Objectives Maximize Power Density (heat generated per unit volume of fuel). Better Neutron Economy (minimize parasitic neutron absorption). High Burnup Potential (maximize energy extraction from fuel). High Temperature Operation (improves thermodynamic efficiency). Considered for research reactors like CIRUS, DHRUVA (e.g., for isotope production, material irradiation). Structural integrity under irradiation and thermal cycling. Fission product retention. Cost-effectiveness. 9. Specific Reactor Fuel Characteristics 9.1 CIRUS Reactor Power: 40 MWT. Fuel: Natural Uranium Metal. Fuel Rod Length: 3 meters. LHR (Linear Heat Rate): 6-14 kW/m. Purpose: Predominantly for isotope fabrication and material irradiation. 9.2 DHRUVA Reactor High Flux Research Reactor. Power: 100 MWT. Fuel: Natural Uranium Metal. Moderator & Coolant: D$_2$O. No fuel cluster (consists of 122 individual fuel rods). LHR: 30-35 kW/m (higher than CIRUS due to higher flux). Fuel temperature: $25^\circ$C (Inlet) to $100^\circ$C (Outlet) for coolant. Fuel surface and center temperatures will be higher. 9.3 Fuel Bundle Design (PHWR) Typical PHWR (e.g., 220 MWe): 19-rod cluster ($1+6+12$ arrangement). OD (Outer Diameter) of fuel rod: 15 mm. Length of fuel bundle: 0.5 m. LHR: 500 W/cm (50 kW/m). Fuel temperatures: Center $\approx 800^\circ$C, Surface $\approx 270^\circ$C. Burnup: 7,500 MWd/t. Clad thickness (Zircaloy): 0.8 mm (collapsible type). Clad is collapsible due to low external pressure and minimal gap, allowing it to swell to meet the fuel. Lower burnup in PHWRs allows for thinner clad compared to free-standing clad in LWRs. 10. Fuel Assembly/Spacer Design Considerations (General & DHRUVA-specific) Spacer should not be overly rigid to allow for differential thermal expansion and accommodate fuel swelling. Design must account for fuel assembly swelling due to irradiation. In DHRUVA, fuel elements have more Aluminum (Al) and less Uranium (U) content in certain regions to manage swelling. Effective cooling water flow for heat removal and neutron moderation. Control/reduction of flow-induced vibrations (FIV) to prevent fretting and wear. Allow for differential thermal expansion between fuel pin and its structural components (e.g., body, end caps). Maintain structural integrity throughout its operational lifetime. Ensure good neutron economy (minimize parasitic absorption by structural materials). Various Spacer Designs: Grid type (common in PWR, BWR). Helical wire wrap (common in Fast Reactors). Split ring spacers (used in some designs). 11. Clad Materials Design 11.1 Desirable Features for Power Reactors: Low neutron absorption cross-section ($\sigma_a$) to improve neutron economy. Good compatibility with the coolant (chemical stability, corrosion resistance). Adequate mechanical properties (strength, ductility, creep resistance) at operating temperatures and under irradiation. High corrosion resistance in the reactor environment. Low porosity (to prevent leakage of fission gases and interaction with coolant). Good thermal conductivity. 11.2 Common Materials: Zircaloy-2 (Zr-2): Alloy of Zr, Sn, Fe, Cr, Ni. Good corrosion resistance. Zircaloy-4 (Zr-4): Similar to Zr-2 but with reduced Ni content to mitigate hydrogen pickup. Widely used in PWRs. Zr-Nb alloys: Offer improved mechanical properties and corrosion resistance, used in some advanced designs. Stainless Steel: Used in some research reactors and early power reactors, higher neutron absorption than Zirconium alloys. 12. Fuel Pin Lattice & Orientation Fuel bundles/assemblies are arranged in a specific lattice pattern within the reactor core. Lattice design influences neutron moderation, heat removal, and overall core performance. Orientation of fuel bundles (e.g., horizontal in PHWRs, vertical in LWRs) affects refueling strategy and support structures. Design is optimized based on: Nuclear aspects: Reactivity, neutron flux distribution, conversion/breeding ratio. Thermal aspects: Heat flux limits, coolant flow distribution, DNB/CHF margins. Mechanical aspects: Structural integrity, resistance to vibration, accommodation of swelling/creep, pellet-clad gap management, plenum size. Irradiation aspects: Material degradation (swelling, creep, embrittlement), fission product retention. 13. Fuel Behavior & Failure Mechanisms 13.1 Fission Gas Release (FGR) Accumulation of gaseous fission products (Xe, Kr) within the fuel matrix. Increases with burnup and fuel temperature. Released gases collect in the fuel-clad gap and plenum, increasing internal pressure. Can lead to clad ballooning and rupture if internal pressure exceeds external pressure and clad strength. Lower density pellets may accommodate more FGR initially but can also release more easily. Excessive FGR can lead to clad failure if not properly managed by plenum volume. 13.2 Irradiation Swelling Volume expansion of the fuel pellet due to the accumulation of solid and gaseous fission products. Increases significantly with burnup. At 10,000 MWd/t, ~4% volume swelling is typical for UO$_2$. Can lead to Pellet-Clad Mechanical Interaction (PCMI) if the swelling fuel contacts the clad. Higher FGR can sometimes reduce overall pellet swelling by releasing gases. Design strategies: Annular pellets, dished pellets, chamfered pellets, and specific L/D ratios to accommodate swelling. 13.3 Thermal Creep & Irradiation Creep Creep: Time-dependent deformation under constant stress at elevated temperatures. Thermal Creep: Primarily temperature-dependent, occurs in both fuel and clad. Irradiation Creep: Enhanced creep rate due to neutron flux, even at lower temperatures. Significant for components like PHWR pressure tubes (PT) and calandria tubes (CT). PT operates at $300^\circ$C and 11 MPa (high stress and temperature). CT operates at lower temperature and pressure. Differential creep causes PT to elongate more than CT. Garter springs are used to maintain separation between PT and CT to prevent contact and localized overheating, which could impair heat transfer. Creep can lead to clad collapse (due to external pressure) or ballooning (due to internal pressure). 13.4 Loss of Ductility (Embrittlement) Neutron irradiation can cause microstructural changes in materials, leading to reduced ductility and increased brittleness. Makes materials more susceptible to fracture under stress. Components like pressure vessels, fuel cladding, and structural materials are affected. Sufficient residual ductility is crucial for the clad to withstand thermal and mechanical shocks during operation. Coolant flow through the annulus of fuel pins helps manage temperature, but clad changes every ~0.1-0.12 years. 14. Thermal Aspects of Fuel Pin Design Thermal Conductivity ($k$): Thermal conductivity of UO$_2$ fuel decreases with increasing temperature. Impacts the temperature profile across the fuel pellet. Temperature Distribution (simplified for uniform heat generation): $T_{center} = T_{surface} + \frac{Q'}{4\pi k}$ Where $Q'$ is the linear heat rate (W/m). Typical Fuel Temperatures: Center $\approx 1800^\circ$C, Surface $\approx 850^\circ$C. Typical Clad Temperatures: Inner surface $\approx 550^\circ$C, Outer surface $\approx 300^\circ$C. Heat transfer from fuel to coolant occurs via conduction through fuel, gap, and clad, then convection to coolant, and sometimes radiation. Helium gas in the fuel-clad gap is used to improve thermal conductivity across the gap. 15. Mechanical Aspects of Fuel Pin Design Pellet Density: Higher density pellets reduce porosity, which lowers the ability to accommodate fission gases internally. Higher density also leads to lower peak fuel temperatures for a given LHR. Optimal density is a balance between FGR accommodation and thermal performance. Pellet-Clad Gap: Initial gap is crucial for accommodating fuel swelling and fission gas release. Too small a gap leads to early PCMI. Too large a gap reduces heat transfer efficiency. Helium gas backfill in the gap enhances thermal conduction. Plenum Size: An empty volume at the end of the fuel stack designed to accommodate released fission gases. Reduces internal pressure buildup within the clad. Pellet-Clad Interaction (PCI): Mechanical contact and interaction between the fuel pellet and the clad. Excessive PCMI can lead to clad stresses and failure. Can be exacerbated by power ramps or rapid changes in power. Loads on Clad: External pressure from the coolant. Internal pressure from fission gases. Thermal stresses due to temperature gradients across the clad. Creep collapse of clad (due to external pressure) or ballooning (due to internal pressure). Clad is often pre-pressurized with helium to counteract external pressure and reduce creep collapse. Axial Gaps: Should be present at various points along the fuel stack to allow for thermal expansion of pellets. Brittle Fracture: Avoidance through proper material selection, design, and operational limits. Feedback Mechanisms: Design must account for interactions, e.g., swelling affecting gap, affecting heat transfer, affecting temperature, affecting FGR. 16. Detailed Fuel Failure Mechanisms Excessive Thermal and Irradiation Swelling: Caused by high pellet density or high burnup. Leads to PCMI, potentially clad stress and failure. Mitigation: Optimize pellet density, use dished/chamfered pellets, control L/D ratio. Overpower: Operation beyond design limits, leading to localized overheating and fuel damage. Can result from reactivity excursions or improper fuel management (e.g., moving a bundle from low to high power zone too quickly). Leads to increased fuel temperature, FGR, and potentially DNB. DNB (Departure from Nucleate Boiling) / CHF (Critical Heat Flux): Occurs when the heat flux from the clad surface becomes too high for the coolant to remove efficiently by nucleate boiling. Leads to a sudden formation of a stable vapor film, drastically reducing heat transfer and causing a rapid, localized rise in clad temperature. Can cause clad overheating and failure. Safety design ensures a sufficient CHFR (Critical Heat Flux Ratio), i.e., ratio of CHF to actual operating heat flux. Stress Corrosion Cracking (SCC): Failure of ductile materials under tensile stress in a corrosive environment. In fuel pins, can occur due to PCMI (mechanical stress) combined with corrosive fission products (e.g., iodine, cadmium) at the clad inner surface. Often initiated during power ramps when stress concentrations are high. Pellet-Clad Mechanical Interaction (PCMI) and Pellet-Clad Chemical Interaction (PCCI) contribute. Hydriding: Absorption of hydrogen by Zirconium alloys, leading to the formation of Zirconium Hydride (ZrH). ZrH is brittle and can lead to clad embrittlement and cracking. Prevention: Minimize moisture content during manufacturing, maintain proper water chemistry, operate below critical temperatures for hydride formation ($150^\circ-200^\circ$C). Fretting Corrosion: Wear and corrosion caused by small amplitude oscillatory motion between contacting surfaces (e.g., fuel rods and spacers) in a corrosive environment. Can lead to clad thinning and eventual perforation. Mitigated by proper spacer design and control of flow-induced vibrations. Creep Rupture: Failure of the clad over long periods due to combined effects of stress, temperature, and irradiation, leading to gradual deformation and eventual rupture. Thermal Fatigue: Repeated thermal cycling (start-ups, shutdowns, power changes) can induce stresses that lead to fatigue cracking in the clad. 17. Power Peaking Factors Measure of non-uniformity in power distribution within the reactor core. Overall Peaking Factor ($P_{overall}$) = $P_{axial} \times P_{radial} \times P_{local}$ Axial Peaking Factor ($P_{axial}$): Ratio of peak to average power density along the core height. To flatten: Use control rods or burnable poisons axially, or vary enrichment axially. Radial Peaking Factor ($P_{radial}$): Ratio of peak to average power density across the core radius. To flatten: Vary enrichment radially (lower enrichment at periphery), use burnable poisons, or place control rods strategically. Local Peaking Factor ($P_{local}$): Peak-to-average power density within a specific fuel assembly or near structural components. Caused by water gaps, moderator gaps, presence of control rods, or structural materials. Can be reduced by burnable poisons (e.g., Gadolinium) or specific fuel rod design. High peaking factors necessitate conservative design limits (e.g., lower average LHR) to ensure the hottest spot does not exceed safety limits. 18. Refueling Strategies Batch Refueling (e.g., LWRs): A fraction (e.g., 1/3 or 1/4) of the core's fuel assemblies is replaced at scheduled intervals (typically 12-18 months). Requires reactor shutdown, depressurization, and cooling down. Fuel assemblies are shuffled to optimize burnup and power distribution (e.g., moving partially spent fuel to less reactive regions). Common patterns: Out-in (fresh fuel at periphery), In-out (fresh fuel at center), Low-leakage (fresh fuel away from periphery). Online Refueling (e.g., PHWRs): Fuel bundles are replaced while the reactor is at full power. Advantages: Higher capacity factor, continuous optimization of power distribution, no costly shutdowns for refueling. Disadvantages: Increased complexity of refueling machinery, potential for fuel handling accidents. Chequerboard/Scatter Pattern Refueling: Bundles are moved from low-power zones to high-power zones to achieve uniform burnup and power distribution. Example: A channel might contain 8 bundles. Bundles are typically pushed in from one end, and spent bundles are discharged from the other. Fuel management strategy aims to reduce neutron leakage and improve overall neutron economy. 19. Redundancy and Diversity in Safety Systems Redundancy: Multiple identical components or systems performing the same safety function. Ensures that if one component fails, others can still perform the function (e.g., multiple safety injection pumps). Provides fault tolerance. Diversity: Use of different principles, technologies, or sensing mechanisms to perform the same safety function. Protects against common-mode failures (where a single event or design flaw could disable all redundant systems). Example: Using both mechanical and hydraulic scram systems, or different types of sensors for a critical parameter. These principles are fundamental in designing robust reactor protection and safety systems. 20. Additional Details & Concepts L/D Ratio of Pellets: Length-to-diameter ratio of fuel pellets. Important for managing thermal expansion and preventing pellet bowing. Pellet-Clad Chemical Interaction (PCCI): Chemical reactions between fuel and clad, often mediated by fission products, leading to clad degradation. Fuel Cycle Length: Duration between refueling outages (for batch refueling) or the average time a fuel bundle stays in the core (for online refueling). Capacity Factor: Ratio of actual power produced to maximum possible power over a period. Online refueling enhances capacity factor. Thermal Shock: Rapid temperature change causing severe stresses, particularly in clad. Burnable Poisons: Neutron absorbers (e.g., Gadolinium, Boron) that deplete over time, used to control excess reactivity and flatten flux. Neutron Leakage: Neutrons escaping the core without causing fission. Minimized by reflectors and proper fuel management. Reflector: Material surrounding the core (e.g., graphite, D$_2$O) that scatters neutrons back into the core, improving neutron economy. Lattice Pitch: Distance between centers of adjacent fuel rods or bundles. Affects moderation ratio and coolant flow. Core Barrel: Cylindrical structure inside the reactor pressure vessel that positions the core. Control Rod Drive Mechanism (CRDM): System for inserting/withdrawing control rods. Containment Building: Structure designed to contain radioactive releases in case of an accident.