Operator Generic Fundamentals Thermodynamics – Core Thermal Limits © Copyright 2014 Operator Generic Fundamentals 2 Core Thermal Limits Introduction • This module covers reactor core thermal limits related to Pressurized Water Reactor plants – Thermal limit purposes – Factors affecting these limits • Core thermal limits are important for ensuring public health and safety during: – Steady-state power conditions – Normal operational transients – During accident conditions such as loss of coolant accidents (LOCA) © Copyright 2014 INTRO Operator Generic Fundamentals 3 Terminal Learning Objectives At the completion of this training session, the trainee will demonstrate mastery of this topic by passing a written exam with a grade of ≥ 80 percent on the following Terminal Learning Objective (TLO): • TLO 1 Describe the reason for reactor core thermal limits and factors affecting them. © Copyright 2014 INTRO Operator Generic Fundamentals 4 Reactor Core Thermal Limits TLO 1 – Describe the reason for reactor core thermal limits and factors affecting them. • The design and operation of a nuclear power plant helps ensure that public health and safety is maintained – Requires maintaining reactor fuel integrity • Requires operating the reactor within established thermal power and peaking limits – Some limits are controlled by the reactor operator – Some are only affected by reactor fuel and material design • Surveillances ensure reactor thermal parameters are in compliance, with corrective action response when required © Copyright 2014 TLO 1 Operator Generic Fundamentals 5 Enabling Learning Objectives for TLO 1 1. Describe the following peaking factors as they relate to local and average reactor power: a. Axial peaking factor (APF) b. Local peaking factor (LPF) c. Radial peaking factor (RPF) d. Total peaking factor (TPF) 2. Describe the reason thermal limits are necessary and the function of the core protection calculator. 3. Describe the factors that affect peaking and hot channel factors. © Copyright 2014 TLO 1 Operator Generic Fundamentals 6 Peaking Factors ELO 1.1 - Describe the following peaking factors as they relate to local and average reactor power: a. Axial peaking factor (APF), b. Local peaking factor (LPF), c. Radial peaking factor (RPF), d. Total peaking factor (TPF) To ensure operation within design limitations, various hot channel and peaking factor limits apply during reactor operation. • Ensure even small localized areas of core power does not exceed design limits. • If exceeded, could cause fuel damage during either – Steady-state operation or transient conditions – Even exceed design criteria for accident condition © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 7 Peaking Factors • The consequences of exceeding any of these prescribed limits could result in β Fuel damage β Clad damage resulting in fission product gases released to the reactor coolant system in an accident condition. β Potential releases to public © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 8 Axial Peaking Factor • Axial peaking factor (APF) is the ratio of: – Average heat flux for a specific elevation (1,2, 3, or 4) to the average heat flux over the entire core • Axial peaking factor is normally defined in plant Technical Specifications as the normalized average axial power at elevation “z” Figure: Simplified Core Map © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 9 Axial Peaking Factor A The information received from the incore map would look as follows: The APF is the ratio of average power density for one elevation to average power density for the entire core. The average power density is determined by adding all individual power density and dividing by number of locations measured. B C D 1 2.0 3.0 2.0 1.0 2 3.0 4.0 3.0 5.0 3 5.0 8.0 6.0 7.0 4 3.0 2.0 2.0 3.0 Figure: Simplified Core Map ππ£πππππ πππ€ππ ππππ ππ‘π¦ = π΄1 + π΅1 + πΆ1 + π·1 + π΄2 + π΅2 + πΆ2 + π·2 + π΄3 + π΅3 + πΆ3 + π·3 + π΄4 + π΅4 + πΆ4 + π·4 16 ππ£πππππ πππ€ππ ππππ ππ‘π¦ = 2+3+2+1+3+4+3+5+5+8+6+7+3+2+2+3 16 ππ£πππππ πππ€ππ ππππ ππ‘π¦ = 3.68 © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 10 Axial Peaking Factor A Referring to the sample core, the power density at elevation “1” is: 2+3+2+1 =2 4 1 2.0 3.0 2.0 1.0 Now APF (Axial peaking factor) can be calculated for our simple core for each core elevation. B C D 1 2.0 3.0 2.0 1.0 2 3.0 4.0 3.0 5.0 3 5.0 8.0 6.0 7.0 4 3.0 2.0 2.0 3.0 APFx = Average power density at Elevation x Average power density 2 3.0 4.0 3.0 5.0 3+4+3+5 = 3.75 4 3 5.0 8.0 6.0 7.0 5+8+6+7 = 6.5 4 4 3.0 2.0 © Copyright 2014 2.0 3.0 3+2+2+3 = 2.5 4 ELO 1.1 π΄ππΉ1 = 2.00/3.68 = 0.543 π΄ππΉ2 = 3.75/3.68 = 1.019 π΄ππΉ3 = 6.50/3.68 = 1.766 π΄ππΉ4 = 2.50/3.68 = 0.679 Slide 10 Operator Generic Fundamentals 11 Axial Peaking Factor • Rod motion and xenon oscillations have strong effects to the average linear power density vertically (Z) in the core – Makes this factor under the control of the operator. Maximum Axial Peaking Factor in the core is calculated based on the core elevation with the highest average kW/ft. π΄π₯πππ πππππππ πΉπππ‘ππ πΉππ = © Copyright 2014 π΄π£πππππ ππ ππ ππ βππππ§πππ‘ππ πππππ π€ππ‘β πππ₯πππ’π ππ‘ ππ‘ ππ π΄π£πππππ ππ π‘βπ ππππ ππ‘ ELO 1.1 Operator Generic Fundamentals 12 Axial Peaking Factor When control rods are inserted into the core, axial peaking factor increases • Control rods initially suppress the neutron flux in the upper portion of the core – Driving the region of peak flux lower in the core • If reactor power is maintained constant – Peak power density increases to compensate for the reduced power densities high in the core • If power is increased with no rod motion – Axial peaking factor will increase due to the primary coolant temperature increase through the core © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 13 Radial Peaking Factor Radial Peaking Factor (RPF) is the ratio of the hottest part of the core to the average power on that horizontal slice – Ratio of the peak heat flux at one core elevation to the average heat flux for that same core elevation: π ππΉ = © Copyright 2014 ππππ πππ€ππ ππππ ππ‘π¦ ππ‘ π‘βπ πππππ‘πππ π΄π£πππππ πππ€ππ ππππ ππ‘π¦ ππ‘ π‘βπ ππππ£ππ‘πππ ELO 1.1 Operator Generic Fundamentals 14 Radial Peaking Factor • Strong function of core design • Under normal conditions, operators have little control of this peaking factor. • Has technical specification limit checked periodically to ensure nuclear heat flux hot channel factor is within prescribed limits. Referring to the sample core below, the average at elevation “1” was previously calculated to be 2.0. The peak power density at elevation “1” is 3.0. (Note this is in assembly B). A π ππΉ1 = 3.0/2.0 = 1.5 B C D 1 2.0 3.0 2.0 1.0 2 3.0 4.0 3.0 5.0 3 5.0 8.0 6.0 7.0 4 3.0 2.0 2.0 3.0 and therefore, π ππΉ2 = 5.0/3.75 = 1.33 π ππΉ3 = 8.0/6.5 = 1.23 π ππΉ4 = 3.0/2.5 = 1.2 © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 15 Local Peaking Factor • Ratio of maximum power at a hot spot to average core power. • Defines the hottest part of a hot nuclear fuel rod. • Assurance that power in a localized area of a fuel rod does not cause melting. • Does not relate to a specific core height (Z) but a hot spot to average core power. πππ₯πππ’π πππ€ππ ππ‘ π π»ππ‘ ππππ‘ πΏππππ πππππππ πΉπππ‘ππ = π΄π£πππππ πΆπππ πππ€ππ © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 16 Heat Flux Hot Channel Factor and Total Peaking Factor • Relates to the maximum local power in the core to the average power in the core. • Max heat flux hot channel factor (HCF) to: – Ensure ability of the ECCS to cool the core following a LOCA – Prevent exceeding specific fuel temperature limits (fuel melting/clad damage). • Limits set by plant’s operating license. • Heat Flux HCF or Total Peaking Factor, πΉπ π – also shown as πΉπ π§ variable for different heights. πΉπ π = © Copyright 2014 πππ₯πππ’π ππππππ πππ€ππ ππππ ππ‘π¦ πππ¦π€βπππ ππ π‘βπ ππππ π΄π£πππππ ππππππ πππ€ππ ππππ ππ‘π¦ ππ π‘βπ ππππ ELO 1.1 Operator Generic Fundamentals 17 Heat Flux Hot Channel Factor and Total Peaking Factor • Sometimes referred to as the ratio of the maximum pellet power generation to the average pellet power generation. • Varies with – Fuel loading patterns – Enrichment – Control rod bank insertion – Fuel burn-up, and – Changes in axial power distribution. © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 18 Heat Flux Hot Channel Factor and Total Peaking Factor In theory, a known value of πΉπ π can determine maximum local power. With an average linear fuel rod thermal power of 5.44 kW/ft. and an πΉπ π known value of 2.32, then the maximum local linear power density anywhere in the core would equal = 2.32 x 5.44 = 12.6 kW/ft. © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 19 Heat Flux Hot Channel Factor and Total Peaking Factor A sub-factor designated as the engineering heat flux HCF (πΉπ πΈ) provides an allowance for manufacturing tolerances on fuel rods, pellets, and cladding. πΉπ π = πΉπ π × πΉπ πΈ © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 20 Heat Flux Hot Channel Factor and Total Peaking Factor πΉπ π, the nuclear uncertainty factor, is a penalty on the measured values of the Radial Peaking Factor, πΉππ π, and the Axial Peaking Factor, πΉπ π. Accounts for the fact that the incore mapping system cannot measure every point in the core – Entirely possible when operating close to πΉπ π limits that a point could exceed this value. πΉπ π = πΉππ π × πΉπ π × πΉπ π © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 21 Heat Flux Hot Channel Factor and Total Peaking Factor Resulting equation for Total Peaking Factor or Heat Flux Hot Channel Factor: πΉπ π = πΉππ π × πΉπ π × πΉπ πΈ × πΉπ π Incore flux mapping system periodically measures the heat flux hot channel factor when the reactor is at or near steady-state conditions. © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 22 Heat Flux Hot Channel Factor and Total Peaking Factor • πΉπ π§ used to represent πΉπ π in the plant technical specifications, • Lowers the limit for the Heat Flux Hot Channel Factor as core height increases. Figure: πΉπ π§ Corrections for Core Height © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 23 Nuclear Enthalpy Rise Hot Channel Factor π The enthalpy rise hot channel factor πΉβπ» is the ratio of the integral of linear power along fuel rod with the highest integrated power to average integrated fuel rod power. Measure of highest total power produced by a fuel rod. Ensures enthalpy rise everywhere in core is low enough to preclude reaching departure from nucleate boiling (DNB). π πΈππ‘βππππ¦ π ππ π π»ππ‘ πΆβπππππ πΉββ © Copyright 2014 ELO 1.1 πΌππ‘πππππ‘ππ ππππππ πππ€ππ ππππ ππ‘π¦ πππππ πππ π€ππ‘β βππβππ π‘ π‘ππ‘ππ πππ€ππ = πΌππ‘πππππ‘ππ ππππππ πππ€ππ ππππ ππ‘π¦ ππ ππ£πππππ πππ Operator Generic Fundamentals 24 Nuclear Enthalpy Rise Hot Channel Factor Fuel loading patterns, enrichments, control rod position, and fuel burnup affect the enthalpy rise hot channel factor. π πΈππ‘βππππ¦ π ππ π π»ππ‘ πΆβπππππ πΉββ © Copyright 2014 ELO 1.1 πΌππ‘πππππ‘ππ ππππππ πππ€ππ ππππ ππ‘π¦ πππππ πππ π€ππ‘β βππβππ π‘ π‘ππ‘ππ πππ€ππ = πΌππ‘πππππ‘ππ ππππππ πππ€ππ ππππ ππ‘π¦ ππ ππ£πππππ πππ Operator Generic Fundamentals 25 Departure from Nucleate Boiling (DNB) Review When amount of steam vapor increases in the coolant channel, the fuel rod cladding is intermittently exposed to steam vapor. When fuel cladding becomes covered with vapor blanket, heat transfer changes from forced convection and nucleate boiling to a combination of conduction and radiation. This condition is called “boiling crisis.” The point of maximum heat transfer rate sustainable with nucleate boiling is called the Departure from Nucleate Boiling (DNB). The point at which DNB occurs is known as the “critical heat flux” (CHF). Figure: Stages of Nucleate Boiling © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 26 Departure from Nucleate Boiling (DNB) Review The consequence of exceeding critical heat flux at any location in reactor core is, in most cases, cladding failure. When critical heat flux is exceeded, transition from nucleate boiling to film boiling occurs rapidly and temperature difference required to transfer heat from surface of fuel rods to reactor coolant increases substantially. Figure: Transition from Nucleate to Film Boiling © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 27 Departure from Nucleate Boiling (DNB) Review Since the temperature of the reactor coolant is fixed, the surface temperature of the fuel rod increases rapidly. If the temperature increase causes the fuel rod cladding to exceed its melting point, a failure, or burnout, will occur. If burnout is to be avoided, a reactor must be operated in a manner to prevent exceeding critical heat flux at any point in the core. Figure: Radial Fuel Temperature Profile © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 28 Departure from Nucleate Boiling Figure: Boiling Heat Transfer Regions Curve © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 29 Peaking Factors Example A PWR core consists of 50,000 fuel rods; each fuel rod has an active length of 12 feet. The core is producing 3,000 MW of thermal energy. If the nuclear heat flux hot channel factor, πΉπ π§ , (total core peaking factor) is 1.8, what is the maximum local linear power density being produced in the core? Solution: 50,000 times 12 feet = 600,000 feet of active fuel rods (3,000 MW x 1,000 kW/MW)/600,000 ft. = 5 kW/ft. 5 kW/ft. x 1.8 = 9 kW /ft. © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 30 Peaking Factors Knowledge Check – NRC Bank A reactor is operating at steady-state conditions in the power range with the following average temperatures in a core plane: Tcoolant = 550°F Tfuel centerline = 1,680°F Assume that the fuel rod heat transfer coefficients and reactor coolant temperatures are equal throughout the core plane. If the maximum total peaking factor in the core plane is 2.1, what is the maximum fuel centerline temperature in the core plane? A. 2,923°F B. 3,528°F C. 4,078°F D. 4,683°F Answer is: A © Copyright 2014 ELO 1.1 Operator Generic Fundamentals 31 Purpose of Core Thermal Limits ELO 1.2 - Describe the reason thermal limits are necessary and the function of the core protection calculator. • For minimal risk to public health and safety, protecting the reactor core, and particularly fuel rod integrity is imperative. • For confidence of maintaining fuel integrity, core operating and core thermal limits are established. • Operation within these limits ensures the plant remains within safety margins that minimize the chance of core (fuel) failure. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 32 Purpose of Core Thermal Limits • Core thermal limits, calculated from the plant safety analysis, are required to ensure fuel cladding integrity during steady-state, transient and accident conditions. • Cladding failure is of prime concern due to its role as the first fission product barrier to the public. Thermal limit criteria ensures there is “at least a 95-percent probability at a 95-percent confidence level” that departure from nucleate boiling (DNB) does not occur on limiting (hottest) fuel rods during normal operation and operational transients, including any transient conditions arising from faults of moderate frequency. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 33 Factors Involved with Reactor Thermal Limits • PWR fuel (UO2) melting point – 5,200°F • Core limits set at 4,700°F – to allow for age and uncertainties • Some fuel pellets may reach 4,000°F during normal operation • If peak central (fuel) temperatures (PCTs) are limited, then cladding temperatures are limited during most analyzed transients and abnormal conditions. • 1,800°F is the threshold of zirconium water reactions (clad) • 2,200°F is the limit set for LOCAs (ECCS criteria) – Point of acceleration of the zirconium water reaction © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 34 Factors Involved with Reactor Thermal Limits • Departure from Nuclear Boiling Ratio (DNBR) – Measure of the probability that DNB is occurring – Ratio of critical heat flux (CHF) to actual heat flux, where CHF is the value of heat flux at which DNB occurs • Typical limit is greater than or equal to 1.3 during steady-state conditions – Limits provide a 95 percent probability at a 95 percent confidence level that the hottest fuel rod does not reach DNB • Fuel cladding design, material, and thickness affects the heat transfer rate from fuel pellet to coolant, and the capability to withstand internal pressure from fission product gases © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 35 Factors Involved with Reactor Thermal Limits • A typical PWR reactor core is limited – To an average linear power density of 5.44 kW/ft. – Localized areas may have a higher peak power with limits of 12.62 kW/ft. – Peak power density during transient operation - 18 kW/ft. • Limits consider: – Limits conservative enough to maintain fuel and cladding temperatures for assurance of fuel integrity. – Fuel cladding integrity ensured by actual heat flux is always less than critical heat flux and DNB does not occur. – Fuel enrichment affects the safety analysis - greater the enrichment the more limiting the thermal limits due to a higher power density. – Materials used in manufacturing the fuel and the design are considered. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 36 Factors Involved with Reactor Thermal Limits • Ability of the ECCS to cool the core following a LOCA combined with the need to prevent exceeding fuel temperature limits (fuel melting / clad damage) dictates the maximum heat flux hot channel factor (HCF) or Total Peaking Factor • During LOCA conditions, HCF limits and ECCS capability together limit fuel damage to criteria set in plant licensing requirements and Nuclear Regulatory Commission regulations: (called ECCS acceptance criteria) – Maximum fuel clad temperature is 2,200°F. – 17% maximum clad oxidation – Maximum hydrogen generation (1 percent of total clad cylinder metal) – Maintaining a coolable core geometry – Able to support long term cooling © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 37 Nuclear Enthalpy Rise Hot Channel Factor • RCS coolant flow rates because of their effect on heat removal. • RCS pressure to maintain subcooling for DNB considerations. • Fuel pellet design and size affect power density and fuel temperature margins. – Smaller pellet has higher core thermal limits due to less power production. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 38 Nuclear Enthalpy Rise Hot Channel Factor • Limits necessary in addition to the Heat Flux HCF to protect the core against reaching DNB. – Because DNB is power density (kW/ft.) and local enthalpy dependent for given plant pressures and flows. • The fuel rod adding the maximum amount of BTUs to the coolant as flow proceeds up the core is the fuel rod where DNB is most likely to occur at some height (Z). – May very well not be, the same fuel rod that has the peak kW/ft. – Point where DNB most likely first occurs will not be in the same horizontal plane as the point of maximum kW/ft. • Limiting DNB will occur at a higher core elevation. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 39 Nuclear Enthalpy Rise Hot Channel Factor π • If the πΉββ is maintained within limits, the minimum DNBR along the hottest rod will be maintained greater than acceptable levels. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 40 Core Protection Calculator Performs the following functions: • Monitor reactor plant operating parameters • Calculate the margins to thermal limits • Trip reactor if either of them is being approached or exceeded – Linear Heat Rate (LHR) greater than 21 kilowatts/foot (kW/ft.) – Departure from Nucleate Boiling Ratio (DNBR) less than 1.26 © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 41 Core Protection Calculator • Fuel rod linear heat transfer rate of 21 kW/ft. maintains the operating temperature below fuel centerline melting temperature. • DNBR greater than 1.26 provides a 95 percent probability with 95 percent confidence that DNB will not occur. • Cladding/fuel melt to extreme temperature increase – Possibly resulting in a breach of the first fission product boundary, and – Release of fission products into reactor coolant. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 42 Core Protection Calculator Consists of four computers to rapidly calculate: – DNBR in limiting coolant channels and – Peak linear heat rates (LHR) in the most limiting fuel rod and take corrective action. • CPC measures reactor power, radial, and axial power shapes to produce three-dimensional power flux shape • Core modeled as twenty horizontal planes or nodes. • Radial power shape calculated as a smooth average power flux shape modified by monitored control rod positions. – Comparing the calculated flux shape to thermal limits avoids localized thermal limit violations due to control rod mispositioning. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 43 Core Protection Calculator • A peak/average ratio for each plane is calculated – Flow rate used in DNBR calculations based on RCP speed, reactor coolant temperatures, and coolant specific volume. • Multiplying axial and radial flux profiles obtains a 3-D flux profile. • Points of maximum LHR or minimum DNBR determined from node point scans. – Comparing obtained values to limits generates reactor trip signals as required. © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 44 Purpose of Core Thermal Limits Knowledge Check The basis for the maximum power density (kW/ft.) power limit is to... A. provide assurance of fuel integrity. B. prevent xenon oscillations. C. allow for fuel pellet manufacturing tolerances. D. prevent nucleate boiling. Answer is: A © Copyright 2014 ELO 1.2 Operator Generic Fundamentals 45 Reactor Operation Effects on Peaking Factors ELO 1.3 - Describe the factors that affect peaking and hot channel factors • Reactor design and operation influence all of the peaking factors; radial, axial, local, total peaking, and enthalpy rise hot channel factors. • Fuel design and enrichment, materials, and power densities considered during reactor design greatly influence the peaking factors and thermal margins. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 46 Reactor Operation Effects on Peaking Factors • During reactor operation, core power distribution and DNBR margins affected by: – Core power – Flux distribution – Fission product poisons – Control rod position – RCS temperatures and pressures • Higher peaking factors and lower DNBR margins mean lower safety margins – Careful monitoring and surveillance of thermal limits important to ensure public health and safety. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 47 Reactor Operation Effects on Peaking Factors • During normal reactor operations, axial peaking factors are within control of the reactor operator. • Control rod motion, reactor power level, and xenon oscillations affect the axial flux profile of the core. – Affecting average linear power density vertically (Z) in the core. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 48 Reactor Operation Effects on Peaking Factors • Normally, the maximum flux is toward the center portion of the core; however, the effects mentioned can cause an up or down flux shift. – Causes increased axial peaking factors. Figure: Axial Flux Profile © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 49 Reactor Operation Effects on Peaking Factors • Certain abnormal reactor operations can cause changes to the axial and radial flux profiles. • A single dropped rod can affect the axial peaking factor, shifting the flux vertically, but – Has larger effect on the radial peaking factor – Especially for a dropped rod away from the center of the core causing one quadrant of the core to produce less power. • Recall that the axial and radial peaking factors make up the total peaking factor: πΉπ π = πΉππ π × πΉπ π × πΉπ πΈ × πΉπ π © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 50 Reactor Operation Effects on Peaking Factors • Since πΉπ π§ is πΉπ π adjusted for height, limits on πΉπ π§ could be reached in the event the flux profile shifts upward. • DNBR is lower near the top of the core because of higher coolant temperatures and slightly lower pressures. β Higher power toward the top of the core lowers DNBR further. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 51 Reactor Operation Effects on Peaking Factors • During plant operations, to ensure DNBR maintained within its limits the following are maintained within operational bands: – Coolant temperatures – Primary pressures – Reactor power level & axial flux profiles – Core flow rates © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 52 Reactor Operation Effects on Peaking Factors • Lowering primary coolant subcooling places the coolant closer to saturation conditions. – At normal full power, primary coolant is approximately 30ο°F subcooled with subcooled nucleate boiling occurring. – If plant conditions reduced subcooling by increased temperatures or decreased pressures, saturated boiling could occur in upper regions of core. • This increases the potential for onset of DNB due to saturated nucleate boiling in upper regions of the core. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 53 Reactor Operation Effects on Peaking Factors • Additionally, with higher primary pressures, a decreased heat transfer rate exists because of a reduction in nucleate boiling. • To maintain the same heat transfer rate (at higher pressures) a larger βT is necessary between the coolant and fuel rod surface temperatures. Figure: Fluid Heat Transfer Regions © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 54 Reactor Operation Effects on Peaking Factors • This means that for a constant power level, fuel temperatures will increase if primary pressure is increased. • Similarly, DNB would occur at smaller οT values at lower pressures, because nucleate boiling occurs sooner at lower pressures with identical power levels. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 55 Reactor Operation Effects on Peaking Factors • A reduction in flow rate, at any power level, increases the temperature of coolant (οT increases, causing Thot to increase). – This also brings the coolant closer to saturation conditions. • Maintaining adequate flow rates is essential to maintaining a minimum acceptable DNBR. • The lower the flow, the less capacity to remove heat. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 56 Reactor Operation Effects on Peaking Factors • High local power densities produce higher heat flux and higher coolant and cladding temperatures. • As a result, heat transfer conditions more closely approach CHF conditions with a reduction in DNBR. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 57 Critical Heat Flux (CHF) • Heat flux associated with DNB • Heat flux that causes DNB to occur for given pressure and temperature conditions. • With increasing differential temperature heat flux reaches a turning point within the nucleate boiling region. – A rapid increase in differential temperature between the heat transfer surface and the liquid – Indicates the heat transfer surface loosing cooling, heating, and potentially causing damage, in this case the nuclear fuel. © Copyright 2014 Information Slide Operator Generic Fundamentals 58 Critical Heat Flux (CHF) • Limits boiling heat transfer use. • Causes physical burnout of the heated surface materials due to: – Sudden inefficient heat transfer rate through a vapor film displacing the liquid adjacent to the heat transfer surface. • When CHF occurs a large increase in the heat transfer surface temperatures occurs. © Copyright 2014 Information Slide Operator Generic Fundamentals 59 Most Limiting Channel • Two basic types of fuel assemblies found in PWR cores are unrodded assemblies and thimble assemblies. • Unrodded assemblies consists of a cross-sectional area bordered by four individual fuel rods. • Thimble cell contains a cross-sectional area bordered by three fuel rods and one thimble guide tube. – The thimble guide tube has wider diameter than typical fuel rod. – This design reduces flow significantly from the unrodded assembly. – Large surface of thimble guide tube has a greater resistance to flow from the large frictional surface. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 60 Most Limiting Channel Figure: Unrodded (Normal) Fuel Assembly and Thimble Fuel Assembly © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 61 Most Limiting Channel • With three instead of four fuel rods, the thimble assembly power production is less. • However, the moderator in thimble cell is relatively cooler than the average coolant temperature across the core. – Causes a peak in thermal neutron flux in the thimble rodlet vicinity. • Because of the thermal neutron flux peak, power density in each of three fuel rods is greater than average power density. • Lower coolant flow and higher power density causes a higher than normal enthalpy rise in thimble assembly channel. – Leads to thimble assembly channels more likely to encounter DNB. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 62 Most Limiting Channel • Several factors can contribute to a fuel channel becoming DNB or hot channel limiting – Clad thickness – Enrichment – Manufacturing tolerances in rod diameter – Fuel pellet dimensions – Crud buildup, and – Non-uniform flow distribution. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 63 Most Limiting Channel • Over core life, the fuel itself changes its thermal performance. – Fuel pellet densification – Swelling – Clad deformation (clad creep), or – Buildup of fission product gases • These can affect the heat transfer to coolant characteristics. – These affect fuel temperatures and cladding temperatures causing a reduction in safety margins. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 64 Most Limiting Channel • Generally, to ensure an adequate safety margin, the worst possible combinations of manufacturing tolerances, highest linear power density, and lower than nominal flows factor into thermal design limits. © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 65 Sample Problem A reactor is operating at steady-state 80 percent power with all control rods fully withdrawn and in manual control. Compared to a 50 percent insertion of one control rod, a 50 percent insertion of a group (or bank) of control rods will cause a __________ increase in the maximum axial peaking factor and a __________ increase in the maximum radial peaking factor. (Assume reactor power remains constant.) A. smaller; smaller B. smaller; larger C. larger; smaller D. larger; larger Answer is: C © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 66 Reactor Operation Effects on Peaking Factors Knowledge Check – NRC Bank Consider a new fuel rod operating at a constant power level for several weeks. During this period, fuel pellet densification in the fuel rod causes the heat transfer rate from the fuel pellets to the cladding to __________; this change causes the average fuel temperature in the fuel rod to __________. A. decrease; increase B. decrease; decrease C. increase; increase D. increase; decrease Answer is: A © Copyright 2014 ELO 1.3 Operator Generic Fundamentals 67 TLO 1 Summary 1. Peaking Factors • Axial Peaking Factor - Rod motion and xenon oscillations have strong effects to the average linear power density vertically (Z) in the core. ππ ππ βππππ§πππ‘ππ ππ‘ ππ πππππ π€ππ‘β πππ₯πππ’π ππ‘ = ππ π΄π£πππππ ππ π‘βπ ππππ ππ‘ π΄π£πππππ π΄π₯πππ πππππππ πΉπππ‘ππ πΉππ © Copyright 2014 TLO 1 Operator Generic Fundamentals 68 TLO 1 Summary • Local Peaking Factor - This is the ratio of maximum power at a hot spot to average core power. • The local peaking factor defines the hottest part of a hot nuclear fuel rod. πππ₯πππ’π πππ€ππ ππ‘ π π»ππ‘ ππππ‘ πΏππππ πππππππ πΉπππ‘ππ = π΄π£πππππ πΆπππ πππ€ππ © Copyright 2014 TLO 1 Operator Generic Fundamentals 69 TLO 1 Summary • Radial Peaking Factor - This factor is a strong function of core design and under normal conditions, operators have little control of this peaking factor. – This ratio has a specific limit periodically verified for compliance with technical specifications. – Ensures that the nuclear heat flux hot channel factor is within prescribed limits. – Measured using the incore system flux mapping system provides a rough approximation of core power distribution status. π πππππ πππππππ πΉπππ‘ππ πΉπ₯π¦ ππ ππ πππ₯πππ’π ππ βππππ§πππ‘ππ πππππ ππππ‘ππππππ π‘βπ πππ₯πππ’π ππ π‘βπ ππππ ππ‘ ππ‘ = ππ π΄π£πππππ ππ π‘βππ‘ π πππ πππππ ππ‘ © Copyright 2014 TLO 1 Operator Generic Fundamentals 70 TLO 1 Summary • Heat Flux Hot Channel Factor (FQ(z)) - relates to the maximum local power in the core to the average power in the core. • πΉπ π is adjusted to core height due to lower DNBR at higher temps and lower pressures – uses term πΉπ π§ . • Affected by fuel design, core loading patterns, control rod position, fuel burn-up, AFD. • πΉπ π is derived from the axial and radial peaking factors, with corrections for uncertainty and engineering factors. πππ₯πππ’π ππππππ πππ€ππ ππππ ππ‘π¦ πππ¦π€βπππ ππ π‘βπ ππππ πΉπ π = π΄π£πππππ ππππππ πππ€ππ ππππ ππ‘π¦ ππ π‘βπ ππππ © Copyright 2014 TLO 1 Operator Generic Fundamentals 71 TLO 1 Summary π • The nuclear enthalpy rise hot channel factor πΉβπ» maximum total power produced in a fuel rod. π πΈππ‘βππππ¦ π ππ π π»ππ‘ πΆβπππππ πΉββ is measure of πΌππ‘πππππ‘ππ ππππππ πππ€ππ ππππ ππ‘π¦ πππππ πππ π€ππ‘β βππβππ π‘ π‘ππ‘ππ πππ€ππ = πΌππ‘πππππ‘ππ ππππππ πππ€ππ ππππ ππ‘π¦ ππ ππ£πππππ πππ • Necessary in addition to the Heat Flux Hot Channel factor to protect the core against reaching DNB. – DNB is power density (kW/ft.) and local enthalpy dependent for given plant pressures and flows. π • If πΉββ is within limits, the minimum DNBR along the hottest rod will be maintained greater than acceptable levels. • The fuel rod adding the maximum amount of BTUs to the coolant as flow proceeds up the core is the fuel rod where DNB is most likely to occur at some height (Z). © Copyright 2014 TLO 1 Operator Generic Fundamentals 72 TLO 1 Summary 2. Purpose of Core Thermal Limits • Reactor fuel integrity ensured by establishing and maintaining core operating limits, and core thermal limits. • Core thermal limits, calculated from the plant safety analysis, are required to ensure fuel cladding integrity during steady-state, transient, and accident conditions. β Cladding failure is of prime concern due to its role as the first fission product barrier to the public. β Thermal limit criteria ensures there is “at least a 95-percent probability at a 95-percent confidence level” that departure from nucleate boiling (DNB) does not occur on limiting (hottest) fuel rods during normal operation and operational transients, including any transient conditions arising from faults of moderate frequency. © Copyright 2014 TLO 1 Operator Generic Fundamentals 73 TLO 1 Summary – Heat flux hot channel factors setpoints for preventing fuel damage following a loss of coolant accidents. o HCF setpoints and ECCS capability together limit fuel damage to criteria set in plant licensing requirements and Nuclear Regulatory Commission regulations. o Maximum fuel clad temperature is 2,200°F., etc. © Copyright 2014 TLO 1 Operator Generic Fundamentals 74 TLO 1 Summary • Peak cladding temperature is limited to 2,200°F to minimize to probability of zirc-water reaction. • PWR fuel (UO2) has a melting point of 5,200°F, core limits are set at 4,700°F to allow for age and uncertainties. Some fuel pellets may actual reach 4,000°F during normal operation. • Typical linear power density limits (Westinghouse): – Steady-state average: 5.44 kW/ft. – Maximum local power density: 12.62 kW/ft. – During transient conditions peak: 18 kW/ft. • Typical linear power density limits (Combustion Engineering): – Steady-state average: 6.2 kW/ft. – Maximum local power density: 10.18 kW/ft. © Copyright 2014 TLO 1 Operator Generic Fundamentals 75 TLO 1 Summary 3. Reactor Operation Effects on Peaking Factors • Operation within the power density limits ensures fuel integrity during normal and transient operations. • Average linear power density is the total thermal power being produced in the core divided by the active length of all the fuel rods and is expressed in kW/ft. • The heat flux necessary to cause DNB for a given set of parameters (pressure, temperature, flow and power) is the Critical Heat Flux (CHF). • Control rod motion, reactor power level and xenon oscillations affect the axial flux profile of the core – axial peaking. © Copyright 2014 TLO 1 Operator Generic Fundamentals 76 TLO 1 Summary • Radial peaking not affected during normal operations – abnormal dropped rod would affect. • During plant operations coolant temperatures, primary pressures, reactor power level, and core flow rates have operational limits to ensure DNBR maintained within its criteria. • Clad thickness, enrichment, manufacturing tolerances in rod diameter, fuel pellet dimensions, crud buildup, and non-uniform flow distribution can contribute to a fuel channel becoming DNB or hot channel limiting. © Copyright 2014 TLO 1 Operator Generic Fundamentals 77 TLO 1 Summary • Over core life the fuel itself changes its thermal performance. β Fuel pellet densification β Swelling β Pellet-cladding interaction (PCI) β Clad deformation (clad creep), or β Buildup of fission product gases • Affect the heat transfer to coolant characteristics – affecting fuel and cladding temperatures possibly causing a reduction in safety margins. • To ensure an adequate safety margins, worst possible combinations of manufacturing tolerances, highest linear power density, and lower than nominal flows factor into thermal design limits. © Copyright 2014 TLO 1 Operator Generic Fundamentals Crossword Puzzle • It’s crossword puzzle time! © Copyright 2014 Summary Operator Generic Fundamentals 79 Terminal Learning Objectives At the completion of this training session, the trainee will demonstrate mastery of this topic by passing a written exam with a grade of ≥ 80 percent on the following Terminal Learning Objective (TLO): • TLO 1 Describe the reason for reactor core thermal limits and factors affecting them. © Copyright 2014 TLO 1 Operator Generic Fundamentals 80 Enabling Learning Objectives for TLO 1 1. Describe the following peaking factors as they relate to local and average reactor power: a. Axial peaking factor (APF) b. Local peaking factor (LPF) c. Radial peaking factor (RPF) d. Total peaking factor (TPF) 2. Describe the reason thermal limits are necessary and the function of the core protection calculator. 3. Describe the factors that affect peaking and hot channel factors. © Copyright 2014 TLO 1 Operator Generic Fundamentals
