Operator Generic Fundamentals Thermodynamics – Core Thermal Limits

Operator Generic Fundamentals Thermodynamics – Core Thermal Limits
K1.01 Radial peaking factor (RPF) K1.02 Axial peaking factor (APF) K1.03 Local peaking factor (LPF) K1.04 Total peaking factor (TPF) K1.05 State the reason thermal limits are necessary. K1.06 Describe the function of the core protection calculator (thermal margin calculator). K1.07 Describe factors that affect peaking and hot channel factors. Operator Generic Fundamentals Thermodynamics – Core Thermal Limits

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. TLO 1

Reactor Core Thermal Limits
TLO 1 – Describe the reason for reactor core thermal limits and factors affecting them. 1.1 Describe the following peaking factors as they relate to local and average reactor power: Axial peaking factor (APF) Radial peaking factor (RPF) Local peaking factor (LPF) Total peaking factor (TPF) 1.2 Describe the reason thermal limits are necessary and the function of the core protection calculator. 1.3 Describe the factors that affect peaking and hot channel factors NOTE: There are not any bank questions on the “core protection calculator” portion of ELO 1.2, however, this material is provided in the Student Guide because it is directly tied to K CPCs are the method used by CE plants to protect themselves from exceeding core thermal limits. Other plants call it Thermal Margin Monitor (TMM), while some call it OTΔT (DNBR protection) or OPΔT (over power protection). Since this isn’t “generic” to all plants, no bank questions exist on that portion of ELO 1.2. The ELO could have been written, “Describe the reason thermal limits are necessary and the method by which this protection is provided”. But only the “reason for thermal limits” is tested by the NRC. We thought it easier to leave the ELO as written to show the tie to the KA. TLO 1

Peaking Factors ELO Describe the following peaking factors as they relate to local and average reactor power: Axial peaking factor (APF), Radial peaking factor (RPF), Local peaking factor (LPF), Total peaking factor (TPF) Core thermal power limits are a function of: Peak value compared to an average value Peak axial flux/average axial flux Peak radial flux/average radial flux Peak change in enthalpy/average change in enthalpy The consequences of exceeding core thermal limits: Fuel clad damage Fission product gases in the RCS Potential releases to public Related KAs K1.01 Radial peaking factor (RPF) K1.02 Axial peaking factor (RPF) K1.03 Local peaking factor (RPF) K1.04 Total peaking factor (RPF) ELO 1.1

Axial Peaking Factor Axial peaking factor (APF) is the ratio of:
Peak axial flux for a specific elevation (1,2, 3, or 4) to the average heat flux over all elevations As shown by: Upper excore detectors/lower excore detectors Incore flux map Several detectors taking snapshots at several elevations Figure: Simplified Core Map ELO 1.1

Axial Peaking Factor For this simplified incore flux map (4 x 4)
APF= Peak Axial Flux (Peak Power Density) Average Axial Flux (Average Power Density) Average Axial Flux Sum of all locations/total number of locations 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦= 𝐴1+𝐵1+𝐶1+𝐷1+𝐴2+𝐵2+𝐶2+𝐷2+𝐴3+𝐵3+𝐶3+𝐷3+𝐴4+𝐵4+𝐶4+𝐷4 16 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦= 3.68 3.0 5.0 2.0 8.0 4.0 6.0 7.0 1.0 A B C D 1 2 3 4 The axial peaking factor, APF, is the ratio of the average heat flux for one elevation to the average heat flux for the entire core. APF is defined in Technical Specifications as the normalized average axial power at elevation “z”. The average heat flux can be determined by using all points. 16 . 3 2 7 6 8 5 4 1 + = 3.68 Figure: Simplified Core Map ELO 1.1 LOI

Axial Peaking Factor APFa = 2.00 / 3.68 = 0.543
B C D 2.0 3.0 2.0 1.0 Referring to the sample core, the power density at elevation “1” is: 1 3.0 4.0 3.0 5.0 2 =2 2.0 3.0 1.0 1 5.0 8.0 6.0 7.0 3 3.0 2.0 2.0 3.0 4 2 𝐴𝑃𝐹2=3.75/3.68=1.019 3.0 4.0 5.0 =3.75 Now APF can be calculated for our simple core for each core elevation. Note the darkness of the red colors show the higher powers. 𝐴𝑃𝐹1=2.00/3.68=0.543 3 𝐴𝑃𝐹3=6.50/3.68=1.766 5.0 8.0 6.0 7.0 =6.5 4 𝐴𝑃𝐹4=2.50/3.68=0.679 3.0 2.0 =2.5 APFa = / 3.68 = 0.543 NOTE: Some values are >1, some < 1. The highest is the “peak elevation”. In this case, the elevation below core midplane (elevation 3) APFb = / 3.68 = 1.019 APFc = / 3.68 = 1.766 APFd = / 3.68 = 0.679 ELO 1.1 LOI

Axial Peaking Factor Peak axial location normally located below core midplane Rods inserted at high power makes that peak worse Xenon oscillations can cause the peak to be high or low High flux peaks could exceed DNBR limits Water closer to saturation higher in core Maximum APF calculated based on the core elevation with the highest average kW/ft 𝐴𝑥𝑖𝑎𝑙 𝑃𝑒𝑎𝑘𝑖𝑛𝑔 𝐹𝑎𝑐𝑡𝑜𝑟 𝐹𝑧 = 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑘𝑊 𝑓𝑡 𝑎𝑡 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑘𝑊 𝑓𝑡 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛𝑠 (𝑐𝑜𝑟𝑒) The actual value used for APF in determining the hot spot is the elevation with the highest average kW/ft divided by the average kW/ft for the core (all elevations). In Tech Specs that value is sometimes called 𝐹 𝑍 𝑁 . ELO 1.1

Radial Peaking Factor Ratio of the peak heat flux at one core elevation to the average heat flux for that same core elevation Excore detectors Which quadrant of Upper and Lower detectors are the highest Incore detectors Which detector at each elevation is the highest Mathematically: 𝑅𝑃𝐹 = 𝑃𝑒𝑎𝑘 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑎𝑡 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑎𝑡 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 ELO 1.1

Radial Peaking Factor Operators have little control of this peaking factor More a function of fuel loading Rods operated in banks/groups 𝑅𝑃𝐹 = 𝑃𝑒𝑎𝑘 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑎𝑡 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑎𝑡 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 𝑅𝑃𝐹1 = = =1.5 Therefore, 𝑅𝑃𝐹2 = 5.0/3.75 = 1.33 𝑅𝑃𝐹3 = 8.0/6.5 = 1.23 𝑅𝑃𝐹4 = 3.0/2.5 = 1.2 3.0 5.0 2.0 8.0 4.0 6.0 7.0 1.0 A B C D 1 2 3 4 ELO 1.1

Local Peaking Factor The first two factors (APF and RPF) determine the “measured” value Local Peaking Factor (LPF), or “engineering” peaking factor (EPF) Specific to plants Some value >1.0 (around 1.1, for example) Consists of design features such as: Pellet diameter, pellet density Cladding diameter Flux map correction factor (incore detector) Not all locations in core are measured by incores Sometimes called “uncertainty” factor ( 𝐹 𝑈 𝑁 ) Multiplied by the “measured” peaking factor to get total peaking factor (TPF) APF x RPF x LPF (EPF) = TPF There are a lot of factors that go into the Local Peaking Factor (or Engineering Peaking Factor). Basically it is a conservative “fudge factor” that means your measured value (APF x RPF) might be closer to limits because of “design and detector inaccuracies”. ELO 1.1

Total Peaking Factor ( 𝑭 𝑸 𝑻 )
Product of “measured” and “local” peaking factors Related to Tech Spec term Heat Flux Hot Channel Factor ( 𝐹 𝑄 𝑍 ) Limits set by plant’s operating license Value is a function of average linear power density Protects from fuel pellet melting During normal, abnormal, and postulated design basis accidents Hot spot (Peak kW/ft) Typical values: Peak kW/ft during normal conditions < 13.6 kW/ft Peak kW/ft during accident conditions < 18 – 22.4 kW/ft Normal and Accident values vary from plant (and fuel) types. Plant specific values can be provided, if desired. ELO 1.1

Heat Flux Hot Channel Factor and Total Peaking Factor
Must know Average Linear Power Density to determine Tech Spec limit Assume the following conditions: Rated MWth = 3411 MW 193 fuel assemblies 264 rods per assembly 12 feet per rod Average Linear Power Density = 5.44 kW/ft ECCS = emergency core cooling system. HCF setpoints and ECCS capability together limit fuel damage to criteria set in plant licensing requirements and Nuclear Regulatory Commission regulations: Maximum fuel clad temperatures 2,200°F. 17 percent maximum clad oxidation Maximum hydrogen generation (1 percent of total clad cylinder metal) Maintaining a coolable core geometry Able to support long term cooling 𝐹 𝑄 𝑧 explained later. ELO 1.1

If normal Peak Linear Power Density limit is 13.6 kW/ft 𝐹 𝑄 𝑇 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑙𝑖𝑛𝑒𝑎𝑟 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑎𝑛𝑦𝑤ℎ𝑒𝑟𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑜𝑟𝑒 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑙𝑖𝑛𝑒𝑎𝑟 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑜𝑟𝑒 𝐹 𝑄 𝑇 = 13.6𝑘𝑊/𝑓𝑡 5.44𝑘𝑊/𝑓𝑡 𝐹 𝑄 𝑇 =2.5 For this plant the Heat Flux Hot Channel Factor (Total Peaking Factor) would be 2.5 Based on value of 2.5, if HOT SPOT < 13.6 kW/ft The rest of the core is within limits ELO 1.1

Peak Linear Power Density (Hot Spot) in core varies with Fuel loading patterns Enrichment Control rod bank insertion Fuel burn-up Changes in axial power distribution Tech Spec value is also height dependent Hotter near top of core Up to 50% core height – full value of TS (2.5) Above 50% core height – some smaller percentage of TS value Westinghouse calls this a factor k(z) from 0 to 1.0. It is derived from the Large Break LOCA to limit decay heat and initial pellet/clad temperatures in the top of the core, which is uncovered first during blowdown and recovered last during reflood. 𝐹 𝑄 𝑧 necessary because DNBR is lower near the top of the core because of higher coolant temperatures and slightly lower pressures. Since 𝐹 𝑄 𝑧 is a variable limit according to core height, the values of the axial and radial peaking factors must also be determined at different core heights for determination of actual 𝐹 𝑄 𝑧 . ELO 1.1

𝐹 𝑄 𝑧 used to represent 𝐹 𝑄 𝑇 in the plant technical specifications Lowers the Heat Flux Hot Channel Factor as core height increases In summation: 𝐹 𝑄 𝑍 = 𝐹 𝑄 𝑇 x 1.0 Up to core midplane 𝐹 𝑄 𝑍 = 𝐹 𝑄 𝑇 x (<1.0) Above core midplane 1 Actual values not shown because they are plant specific. Plant specific values can be obtained from your Core Operating Limits Report (COLR) and show here, if desired. Summarize the components of the Heat Flux Hot Channel Factor (last few slides): Axial Peaking Factor(APF) x Radial Peaking Factor(RPF) x Engineering Correction factor(LPF) = Total Peaking Factor(TPF). Total Peaking Factor(TPF) x Height Correction Factor must be less than Heat Flux Hot Channel Factor( 𝐹 𝑄 𝑍 ) Figure: 𝐹 𝑄 𝑧 Corrections for Core Height ELO 1.1

Nuclear Enthalpy Rise Hot Channel Factor
The Nuclear Enthalpy Rise Hot Channel Factor 𝐹 ∆𝐻 𝑁 is: A measure of maximum total power produced in fuel rod Coolant flowing next to a high power fuel rod has larger enthalpy rise than a lower power fuel rod Important when mixing new fuel with 1/3 or 2/3 used fuel during refueling loads Measurements obtained from in-core detection system Analyzed by computer to determine factor Factor dependent on fuel loading patterns, bank insertion, and fuel burn-up This Tech Spec required value is much easier to understand. Basically take the kW/ft for a given flow channel times 12 ft and you get the total kW. ELO 1.1

Ensures departure from nucleate boiling (DNB) not reached or, Average linear power density rod (based on previous example) 5.44kW/ft x 12ft = 65.28kW This Tech Spec required value is much easier to understand. Basically take the kW/ft for a given flow channel times 12 ft and you get the total kW. ELO 1.1

Typical Tech Spec Value is 1.8 Based on average power density rod of kW Peak rod would be x 1.8 = kW May not be the same channel as the fuel rod with 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 Peak kW/ft normally below core midplane Minimum DNBR normally above core midplane ELO 1.1

Departure from Nucleate Boiling (DNB) Review
Tcold enters all flow channels at approximately the same temperature Heat is added (kW/ft) to the water as it moves up the core The more heat added, the higher the temperature The higher the temperature, the closer to DNB The closer to DNB, the lower the overall heat transfer coefficient The lower the overall heat transfer coefficient, the higher the fuel centerline temperature The higher the fuel centerline temperature, the higher the cladding temperature The higher the cladding temperature, the more likelihood of cladding oxidation End result More likelihood of fuel damage, release of fission products This is a brief review of what was discussed in the last chapter relating to DNB. ELO 1.1 LOI

Fuel Rod Temperature Profile
Assuming the heat production per unit volume throughout the pellet is uniform, the linear power density in kW/ft is proportional to the difference between the centerline temperature and the bulk fluid temperature Tcenterline Tbulk Q” This is not exactly the case, since the thermal neutron flux is higher on the outside of the pellet and lower in the center due to absorption. 𝑄 ′∝ (Tcenterline − Tbulk) ELO 1.2

Peaking Factors Knowledge Check – NRC Bank
A PWR core consists of 50,000 fuel rods; each fuel rod has an active length of 12 feet. The core is producing 1,800 MW of thermal power. If the total heat flux hot channel factor (also called the total core peaking factor) is 3.0, what is the maximum linear power density being produced in the core? 4.5 kW/ft 6.0 kW/ft 9.0 kW/ft 12.0 kW/ft Correct answer is C. Correct Answer is C. NRC Bank Question – P4949 Analysis: The nuclear heat flux hot channel factor, FQ(z), (also called the total core peaking factor) is a function of the peak to average power. Measurements for this parameter can be obtained using in-core detectors taking a series of measurements across the full length of the core, and determining the ratio of peak flux for one elevation to the average flux for all elevations. Average linear power density:1800 x 1000/50000 x 12 = 3.0 kW/ft. Peak linear power density: 3.0 kW/ft x 3.0 (peaking factor) = 9.0 kW/ft Choice “C” is correct ELO 1.1

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? 2,923°F 3,528°F 4,078°F 4,683°F Correct answer is A. Correct answer is A. NRC Question P6249 Analysis: Keep in mind that this question is still looking at a Peaking Factor = Peak/Average. Instead of power it is looking at peak/average fuel centerline temperatures. Even though there might not be a linear correlation to power and fuel centerline temperatures, this “basic” concept still applies. The average Delta-T for the above question is 1680°F – 550°F = 1130°F. Based on a provided peaking factor (2.1), that relates to a peak Delta-T of 1130°F x 2.1 = 2373°F. To determine Tfuel centerline, merely add the peak Delta-T of 2373°F to the Tcoolant temperature of 550°F to get 2923°F. Therefore, choice “A” is correct. ELO 1.1

Purpose of Core Thermal Limits
ELO Describe the reason thermal limits are necessary and the function of the core protection calculator. Ultimate Goal Protect health and safety of the public 10CFR 100 radiation limits Local goal Maintain fuel cladding integrity during normal and accident conditions Thermal limit of 2200°F is imposed as peak cladding temperature Cladding subject to excessive reaction of zirconium and water at temperatures above 2200°F Limit protected by maintaining DNBR limits Nuclear Enthalpy Rise Hot Channel Factor (DNBR) Related KAs K1.05 State the reason thermal limits are necessary , K1.06 Describe the function of the core protection calculator (thermal margin calculator). There are not any questions relating to K1.06 since it is specific to CE plants and not “generic” in nature. Information about the Core Protection Calculator (CPC) is provided in the Student Guide. The second part of this ELO will be briefly discussed as “how can we protect ourselves from exceeding core thermal limits”, as opposed to a specific plant’s method (CPC). ELO 1.2

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 By limiting peak central (fuel) temperatures (PCTs) cladding temperature limits are not exceeded 1,800°F is the threshold of zirconium water reactions (clad) 2,200°F is the limit set for LOCAs (ECCS criteria) PCT = Peak Central (fuel) Temperature ELO 1.2

Departure from Nuclear Boiling Ratio (DNBR) Ratio of critical heat flux (CHF) to actual heat flux (AHF) Typical limit is > 1.3 during steady-state conditions Provided a 95% probability that 95% of the fuel is not experiencing 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 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 ELO 1.2

ECCS Acceptance Criteria
Each ECCS design must demonstrate the capability to maintain core conditions within five general limits in the event of a worst-case LOCA (10 CFR 50.46) Maximum fuel clad temperature - 2,200°F Clad oxidation < 17% clad thickness Maximum hydrogen generation - 1% Maintaining a coolable core geometry No gross cladding failure Able to support long term cooling Cold Leg Recirc and Hot Leg Recirc These criteria are for LOCA accident conditions NOT normal operations. Coolable Geometry: If cooling flow is lost to the core resulting to cladding failure, restoration of cooling flow might not have flow channels to flow through and remove decay heat. Long Term Cooling: LBLOCA of a cold leg could result in boron precipitating off near the bottom of the core, possibly restricting flow. Switching to Hot Leg Recirc, flow is from Hot Leg to Cold (backwards through the core) breaking up any boron that precipitated out. ELO 1.2

How Are We Protected? If limits exceeded, power must be lowered
“Reactivity” is the most important parameter to control Quick transients (results in plant trips) High power trip Prevent fuel pellet melting Low pressure trip Prevent DNBR conditions Low Flow Trip Prevent fuel pellet melting or DNBR conditions Slow Transients (might result in plant runback, or trip) Slow depressurization of RCS DNBR concern Protections vary from plant to plant as well as plant type. The above is generic in nature and plant specifics can be presented briefly here if desired. CE plants might use some sort of CPC or Thermal Margin Monitor to protect from the “slow transients”, while Westinghouse plant uses OPDT or OTDT trips/turbine runbacks ELO 1.2

Knowledge Check What is the basis for the limit on maximum linear power density (kW/ft)? To provide assurance of fuel integrity. To prevent xenon-135 oscillations. To allow for fuel pellet manufacturing tolerances. To prevent nucleate boiling. Correct answer is A. Correct answer is A. NRC Bank Question – P56 Analysis: CORRECT. Limiting the maximum power density (kW/foot) provides assurance that the centerline of the pellet does not melt, which expands the pellet and creates a breach of the first fission product barrier (fuel cladding). Keeping the fuel cladding intact is paramount to protecting the health and safety of the public. If the first fission product barrier were compromised, significant increases would be noted in RCS fission product activity. If the maximum power density (kW/foot) power limit is exceeded at a local “hot spot”, fuel pellet melting could occur. This would result in cladding damage and release of fission products in the RCS. B. WRONG. Maintaining the maximum power density (kW/foot) does not prevent Xenon oscillations from occurring in the core. Xenon oscillations are caused by changes in Xe-135 concentration in the core that can be caused by control rod insertion. C. WRONG. Fuel pellet manufacturing tolerances are accounted for in fuel loading, not maintaining linear heat rate within specification. D. WRONG. Keeping the departure from nucleate boiling ratio (DNBR) within its acceptable value (GFES uses > 1.3) ensures that nucleate boiling does not occur. This is a separate parameter from linear power density (LPD) or linear heat rate (LHR). ELO 1.2

Knowledge Check Peaking (or hot channel) factors are used to establish a maximum reactor power level such that fuel pellet temperature is limited to prevent __________ of the fuel pellets; and fuel cladding temperature is limited to prevent __________ of the fuel cladding during most analyzed transients and abnormal conditions. melting; melting excessive expansion; melting melting; excessive oxidation excessive expansion; excessive oxidation Correct answer is C. Correct answer is C. NRC Bank Question – P1194 Analysis: NOTE: Keep in mind that the concern of fuel pellet melting is that it will still cause cladding temperature to exceed its limits. Maximum reactor power limits (kW/ft peak power) is provided to prevent fuel pellet melting. Fuel cladding temperature (DNBR) is limited to prevent cladding oxidation. At approximately 2,200ºF the reaction rate of the zircaloy-steam reaction increases rapidly, producing excess amounts of Hydrogen gas: Zr + 2 H2O ZrO2 + 2 H2 Note that this reaction is endothermic (requires heat to occur). Therefore, as temperature increases, the reaction produces Hydrogen gas at a faster rate. Ensuring a maximum of 2,200ºF during post-accident conditions is required by 10 CFR Even if hydrogen gas production is small enough to not make an explosive environment in containment, the 2200°F clad temperature limit is still a concern because it causes the cladding to oxidize, making it more susceptible to failure. ELO 1.2

Reactor Operation Effects on Peaking Factors
ELO Describe the factors that affect peaking and hot channel factors. Tech Spec peaking factor limits are affected by: Core power/ Flux distribution Control rod position RCS flow and most limiting channel RCS temperature RCS pressure Time in core life Higher power peaking or lower DNBR means lower safety margins Related KA K1.07 Describe factors that affect peaking and hot channel factors ELO 1.3

Reactor Power Effects High power means high flux
Actual Heat Flux increases High flux means high temperatures Critical Heat Flux decreases As a result Closer to peak kW/ft and DNBR limits 𝐷𝑁𝐵𝑅= 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 ℎ𝑒𝑎𝑡 𝑓𝑙𝑢𝑥 𝑎𝑐𝑡𝑢𝑎𝑙 ℎ𝑒𝑎𝑡 𝑓𝑙𝑢𝑥 ELO 1.3

Flux Distribution Effects
Axial Flux Distribution (AFD) not applicable below 50% power Peaking less of a concern when total flux is low The following factors can effect flux distribution Control rod motion Reactor power level Xenon oscillations ELO 1.3

Normally, peak flux is toward the center portion of the core Slightly below core midplane Previous factor changes can increase axial peaking factors Figure: Axial Flux Profile ELO 1.3

Recall 𝐹𝑄(𝑧) is 𝐹𝑄𝑇 adjusted for height Limits on 𝐹𝑄(𝑧) could be reached if the flux profile shifts upward Recall minimum DNBR slightly above core midplane higher coolant temperatures and slightly lower pressures Higher power toward the top of the core lowers DNBR further Lower pressure because of pressure drop across the reactor vessel. ELO 1.3

Control Rod Position Effects
Rod insertions can cause changes to the axial and radial flux profiles Total Peaking Factor impacted by Axial and radial Peaking Factors Impacts vary based on “single” rod or “bank” of rods Effects on Axial versus Radial Keep in mind that there were also several bank questions on this concept in the Control Rod section. ELO 1.3

Single rod inserted 100% versus a single rod inserted 50% Axial Peak/Average impact Bigger impact inserted 50% If inserted 100% it is a uniform poison (effects ALL axial elevations) Radial Peak/Average impact Bigger impact inserted 100% Depresses more flux in that quadrant if fully inserted Keep in mind that there were also several bank questions on this concept in the Control Rod section. ELO 1.3

Single rod inserted 50% versus Bank of rods inserted 50% Axial Peak/Average impact Bigger impact if bank of rods inserted 50% Depresses more flux downward with bank of rods inserted Radial Peak/Average impact Bigger impact if single rod inserted 50% Bank of rods effects ALL quadrants Keep in mind that there were also several bank questions on this concept in the Control Rod section. ELO 1.3

RCS Flow Effects A reduction in flow rate, at any power level
Increases the temperature of coolant T increases, causing Thot to increase Coolant closer to saturation conditions Closer to peaking factor limits No decrease in flow acceptable Rx trip on any reduction in RCP flow Hottest channel, however, might have flow restrictions Thimble Guide Tubes, instrumentation Determining most limiting flow channel is important Closer to DNBR ELO 1.3

Figure: Unrodded (Normal) Fuel Assembly and Thimble Fuel Assembly
Most Limiting Channel Two basic types of fuel assemblies found in PWR unrodded assemblies thimble assemblies Unrodded assemblies consists of area with four individual fuel rods Thimble cell contains three fuel rods and one thimble guide tube The thimble guide tube has wider diameter than typical fuel rod reduces flow significantly from the unrodded assembly Figure: Unrodded (Normal) Fuel Assembly and Thimble Fuel Assembly ELO 1.3

Most Limiting Channel With three instead of four fuel rods
Thimble assembly power production is less Results in lower flux Slightly cooler temperature Results in higher flux Also results in three fuel rods with greater than average power density Lower coolant flow and higher power density causes Higher than normal enthalpy rise in thimble assembly channel Leads to thimble assembly channels more likely to encounter DNB ELO 1.3

Most Limiting Channel Several other factors also contribute to most limiting channel Clad thickness Enrichment Manufacturing tolerances in rod diameter Fuel pellet dimensions Crud buildup Non-uniform flow distribution 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. ELO 1.3

RCS Temperature Effects
RCS temperature a function of reactor power Power increases, temperature increases At normal full power, RCS ≈ 30F subcooled If temperature allowed to be high in program band More saturated boiling could occur in upper regions of core Higher the RCS temperature Closer to DNB ELO 1.3

Primary Pressure Effects
At normal full power, RCS ≈ 30F subcooled If RCS pressure decreases Closer to saturation conditions Critical Heat Flux lowers with decreases pressure Pool Boiling Curve lowers and shifts to left Operating closer to DNB Use the boiling heat transfer curve to point this out with increasing temperatures to maintain the same heat flux. Changes to curve when pressure decreases are animated on clicks/automatic. Figure: Fluid Heat Transfer Regions Initial Hottest Operating Point Initial Margin to DNB New Margin to DNB after lowered pressure ELO 1.3

Time in Core Life Effects
Over core life, the fuel itself changes its thermal performance Fuel pellet densification Pellet Swelling Clad deformation (clad creep), or Buildup of fission product gases Over core life, flux shift out axially and radially from center of core Slightly improves the Peak/Average flux distribution ELO 1.3

Fuel Densification Occurs within first 200 hours of cycle operation
arises from the elimination of small pores in the UO2 pellets Gap thickness increases, resulting in A decrease in heat transfer Increase of the overall DT Increase in fuel centerline temperature Also, with “denser” pellet Linear power density increases Same kW, smaller area, higher kW/ft Fuel densification might limit initial power ascension rate Eventually fission products cause pellet to swell Pellet swell and clad creep discussed on next slide ELO 1.3

Pellet Swell and Clad Creep
Production of fission gases cause a gradual swelling of the fuel pellets, resulting in Smaller Dt gap, Smaller overall DT, lower fuel temperature Clad Creep RCS pressure acting on cladding causes Decreased fuel-to-clad gap, decreased DTgap, overall DT, and lower fuel temperature Overall Effect of Creep and Swell Over core life Slightly better heat transfer from fuel to coolant Slightly lower fuel centerline temperature ELO 1.3

Effects on Peaking Factors Summary
Coolant Temperature Higher temperature, closer to DNB Coolant Pressure Lower pressure, closer to DNB Core Flow Rates Lower flow rates, closer to DNB Reactor Power Level Higher power, closer to DNB or Peak kW/ft Flux Distribution Higher the Peak/Average, closer to DNB or Peak kW/ft ELO 1.3

Knowledge Check 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.) smaller; smaller smaller; larger larger; smaller larger; larger Correct answer is C. Correct answer is C. NRC Bank Question – P1095 Analysis: APF LARGER: A bank of control rods inserted 50 percent will have a larger affect on axial peaking factor, than a single control rod inserted 50 percent; the core flux peak will be pushed down in the entire core versus in just the quadrant that the single rod is located in. The same amount of power is being generated in the core in a smaller area, the average power density will be higher in the flux peak, thus the APF will be higher in that area RPF SMALLER: Inserting one control rod 50 percent will suppress the neutron flux in that quadrant and slightly in the adjacent two, the furthest quadrant from the inserted rod will have a higher peak power density (to maintain the same power level). When a bank of control rods is inserted the RPF will increase in the un-rodded sections of the core, but in a more uniform manner (all 4 quadrants effected), and the resultant increase in RPF will be less than the change associated for a single control rod inserted 50 percent. ELO 1.3

Knowledge Check 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 __________. decrease; increase decrease; decrease increase; increase increase; decrease Correct answer is A. Correct answer is A. NRC Question P6449 Analysis: Densification is generally attributed to the elimination of small pores in the fuel rods, resulting in an increase in pellet-to-clad gap. One byproduct of the increase in pellet-to-clad gap, is reduced thermal conductivity. This causes the heat transfer rate from the fuel pellets to the cladding to decrease. This results in a slight increase in fuel temperature. ELO 1.3

NRC KA to ELO Tie KA # KA Statement RO SRO ELO K1.01
Radial peaking factor (RPF) 2.3 2.8 1.1 K1.02 Axial peaking factor (APF) K1.03 Local peaking factor (LPF) 2.2 2.7 K1.04 Total peaking factor (TPF) K1.05 State the reason thermal limits are necessary. 3.1 3.5 1.2 K1.06 Describe the function of the core protection calculator (thermal margin calculator). 3.7 K1.07 Describe factors that affect peaking and hot channel factors. 2.9 3.3 1.3

Operator Generic Fundamentals Thermodynamics – Core Thermal Limits

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Operator Generic Fundamentals Thermodynamics – Core Thermal Limits

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