Read: BWR Section 3 (Assigned Previously) PWR Chapter (Assigned Previously) References: BWR SAR Section 4.4 PWR SAR Section 4.4 Principal Design Requirements (1) Energy Costs Minimized A) Maximize Plant Thermal Efficiency Thermal-Hydraulic Design As known from basic thermodynamics, this implies maximizing the temperature difference between the source and sink. or the reactor core, this translates into making the coolant (HO) outlet temperature as high as possible, but not violating thermal constraints. Material constraints (crud deposition on clad) also enter. B) Increase Core Power Density (kw/liter) We desire to make the core as compact as possible, thereby reducing pressure vessel size and hence plant investment fixed charges/kwhr. Aided by a flat power profile provided by the Nuclear Design (ND). C) Increase uel Specific Power (kw/kg-u) or a fixed thermal output, increasing the fuel specific power results in less kg-u required, and hence reduced fuel costs. Once again thermal limitations will constrain the fuel specific power. () Safety Criteria Satisfied This is concerned primarily with maintaining the clad s integrity under accident conditions. High fuel or clad temperature, high fuel rod internal pressure or mechanical movement of the assemblies could all lead to clad perforation and resulting fission product release. Certain chemical reactions between the materials in the core must also be prevented, which occur at high temperatures.
Design Limitations A design must be produced that, during normal and abnormal operation does not violate: A) Maximum allowed fuel temperature, determined by: (I) Centerline melt (conservatively set to 4700 O for un-irradiated UO) => fuel slumps, contacts and fails clad (II) uel Pellet Clad mechanical Interaction (PCI) => fuel heats up and expands making contact with clad. Neutron irradiation embrittles the cladding making it susceptible to cracking. Local increases in clad temperature can also be an issue. (III) Maximum allowed rod internal pressure, dictated by clad burst limit (IV) Maximum allowed clad temperatures, as limited by: (a) Exceeding the Critical Heat lux (CH) PWR: Departure from Nucleate Boiling (DNB) DNB Dominated low Boiling Curve Bubble density on the rod surface becomes sufficiently high to impede liquid return to the surface leading to transition to stable film boiling. DNB is a complicated function of flow rate, coolant temperature and pressure, quality, inlet enthalpy and equivalent flow diameter. Correlations are obtained from experiments, such as the W-3 correlation of L.S. Tong.
BWR: Dryout Dryout Dominated low Boiling Curve If flow conditions allow the transition to annular flow, increases in heat flux can lead to dryout of the liquid film and transition to single phase forced convection with a superheated vapor Less severe temperature excursion than DNB since high steam velocities provide some cooling, however can still exceed clad material limits As with DNB, CH (or CPR) predicted by correlations based on experimental data (CISE or GE GEXL)
In general CHDNB > CHDryout Implication: Core Average Heat lux = Power Generated in Average uel Rod = (π*clad Radius*Length) Q N f rods 1 D H o = Linear Power Rating (kw/ft) = (π*clad Radius) Q f 1 N H D rods o or same kw/ft rating: => (Clad Radius)PWR < (Clad Radius)BWR (b) Loss of Coolant Accident (LOCA) The clad temperature resulting from the temporary loss of coolant is highly dependent on the Emergency Core Cooling System (ECCS). This is a complicated area treated by specialist. The normal function of the core T/H designer is to minimize initial stored energy in the fuel by minimizing fuel temperatures. (B) Maximum Allowed Coolant Pressure To increase thermal efficiency and avoid exceeding CH and Bulk Boiling (for a PWR), the T/H designer desires high coolant pressures. Increased pressures allow for higher coolant temperatures. But TCoolant => TClad => Cladding corrosion. BWR: TCoolant = Tsat(PCoolant), PCoolant~1000 psia PWR: Max TCoolant=Tsat(PCoolant)-ΔTSubcooling, PCoolant~50 psia (PWR higher pressure to suppress boiling in primary loop and allow high core outlet temperature, to transfer energy across steam generator)
(C) Lift and Jetting orce Constraints (I) Due to flow resistance, the fuel assembly is subjected to hydraulic forces. The T/H designer must assure that the assembly will not be lifted or individual components distorted. Example: PWR has about 0-30 psi drop across core. (II) Jetting occurs when an internal core structure (or transverse ΔP exists) forces the coolant to flow perpendicular to its normal vertical flow direction at high velocity. Such jetting can impinge on an individual fuel rod and cause clad failure by erosion or vibration. Grids and core baffle plates (surround outside assemblies) should be such as to avoid undue jetting. (D) Hydrodynamic low Stability This involves the coolant flow stability as dictated by cross-flow behavior caused by lateral pressure (and density) gradient effects PWR: Instability avoided by restricting maximum allowed quality of coolant BWR: Instability avoided by employing canned assemblies (restricting cross flow), imposing Power-low limits (remember core flow rate variable via recirculation system), and using inlet orifices Interconnection with Material/Mechanical Design (M/M) Many of the calculations performed by T/H design depend on the behavior of the fuel rod under irradiation and thermal stress. M/M design therefore provides information about: (1) fuel swelling and material degradation effects on fuel melting temperature, fuel thermal conductivity and clad-fuel interface (gap) size () clad deformation (3) fission product release to gap (effects gap thermal conductivity and internal rod pressure)
Thermal/Hydraulic undamentals: uel Rod Heat Transfer uel Rod Cross Section Clad R uel Ro Ri Gap uel/gap/clad Gap behavior is a complicated function of burnup. Gap conductance (resistance) is a function of the fission gas inventory and pellet/clad contact pressure. Gap conductance obtained empirically from experimental data.
Volumetric Heat Generation Rate (Power Density) q( r) G ( r, E) ( r, E) de 0 f Linear Heat Rate q( z) q( r) da q( r, z) rdr q( z) R A x R 0 Cylindrical Rod Uniform Radial Distribution Heat lux q ( z) Do dz q( z) dz q( r) da dz q( z) R dz A x Uniform Radial Distribution Cylindrical uel Rod
uel Temperature Behavior Neglecting axial conduction and assuming a radially uniform volumetric heat generation rate (power density), the conduction equation in the fuel is 1 d dt rk ( T ) q 0 rdr dr Multiply by r and integrate from r = 0 to some r = r r d dt rk ( T) dr qrdr 0 dr dr 0 0 r dt dt qr rk ( T) rk ( T) 0 dr dr r r 0 0 dt qr rk ( T) 0 dr Divide by r and integrate from r = 0 to the pellet radius dt qr k ( T) 0 dr R dt qr k ( T ) dr dr0 dr 0 0 R Assume k ( T) k, i.e. constant fuel thermal conductivity qr k[ T( R) T(0)] 0 4 qr q T(0) T( R) T 4k 4 k In addition 1 1 R 1 o q 1 1 R o 1 T( R) T q( Ro) Ro ln ln H G R i k c R i h c R o H G R i k c R i h c R o
q( Ro ) q Tc( Ro) T h R h c o c Conclusion: Temperature rise at any point across a fuel rod is proportional to the linear heat rate. With the fuel pellet surface temperature fixed (nearly) by coolant conditions and the maximum fuel temperature limited by melting, this implies T max known, hence max q allowed bounded by q k T max max 4 Relaxing the assumption of constant fuel thermal conductivity, MELT T max q 4 k T dt T R Conductivity Integral *This integral has been experimentally measured under irradiation conditions. MELT inal Conclusion: T, coolant temperature (relates to T(R)) and fuel thermal conductivity uniquely specify the maximum linear power rating, nearly independent of pellet O.D. or UO: max( q ) 0 3 kw/ft Hot Spot of core, i.e. highest power density pellet, limits the entire core. Implication: Nuclear Designer desires to flatten the spatial power distribution. Complications: k(t), gap conductivity, convective heat transfer coefficient, internal rod and overall core power distribution all change with time (burnup). Hence one must design to worst condition throughout core life. How is max( q ) value that produces centerline fuel melt temperature used? To assure overpower reactor protection system trip setpoint has appropriate value, which protects fuel for accident situations.
Representative PWR uel Temperatures at BOC as a unction of Linear Heat Rate
What limits q during normal operating conditions? LOCA: uel stored energy and fission product decay heat ( q ) dictate that q not exceed a specified value or else cladding temperature will exceed temperature limit (inal Acceptance Criteria limits cladding temperature to 00 o ). max ( q) nominal max ( q) 0.07 LOCA Decay Heat raction Typical max ( q ) value allowed during normal operation 15 kw/ft rom neutronics calculations, Nuclear Designer (ND) can tell T/H designer what is peak-toaverage power density in a core of a given size and loading pattern Total Peaking actor (Denoted q) = Maximum Power Density/ Average Power Density LOCA Limit impact on Maximum Core Thermal Output ( Q ) RX q core QRX NrodsH f max ( q) nominal q f ( N H) rods How is Q matched to required power, e.g. RX RX target RX Q ( Q ) (1) Reduce q by revised loading pattern choice (and for BWRs control rod program) ND responsibility () Increase length of all fuel in the core (NrodsH), which implies: (A) More fuel assemblies of same length and diameter rods (larger core and vessel) or longer assemblies employed (B) Smaller diameter rods such that more length of fuel in a given assembly footprint PWR: q.0-.8 Core Average kw/ft 5.4-6.7 BWR: q.0-.6 Core Average kw/ft 4.5-7.1
Determination of fuel pin radius q 1 uel Specific Power where U is the U density in UO R R U Desire high fuel specific power for low capital cost => minimize fuel pellet radius: Limitations on smallness of R: (1) Structural fuel pellet and surrounding clad (fuel rod) must form a sound structural unit Typical uel Rod Length 1 ft. If R is too small, the assembly design would require much more support, increasing manufacturing cost and fuel costs (poorer neutron economy due to structural materials). Tolerance control would also be difficult. () CH Limitation: q Rod Surface Heat flux, where R o = clad outer radius Ro Decreasing R decreases the clad OD, hence increases the heat flux, which must be below the CH value. Conclusion: R must be large enough to avoid exceeding CH or a given linear heat rate R specific power but CHR Pick smallest R such that CH limits are met. Resulting Values of uel Pin Radius: PWR: (0.19-0.1 ) for 17x17 15x15 BWR: (0.17-0.8 ) for 10x10 8x8 because (CH)PWR > (CH)BWR uel Specific Power: PWR: 38 kw/kg BWR: 5 kw/kg
Determination of Gap Size Considerations: (1) Gap size should be minimized for good heat transfer and structural rigidity () Gap size should be maximized to simplify manufacturing (tolerances) Compromise: (1) Pressurize rod initially with He (few atm (BWR) to 450 psia (PWR)) to increase heat transfer and minimize pressure on clad () Design upper plenum to reduce internal pressure buildup with burnup (3) Allow sufficient gap for ease of manufacturing In reality for a PWR, clad creeps down onto fuel in a few 1000 hours of operation due to primary system pressure. Gap sizes: PWR: 6 mils (Cold) BWR: 3.5 (hot) -1 (Cold) mils Determination of Clad Thickness Considerations: (1) Thick enough to add structural support () Thick enough to retain fission products and protect fuel from moderator. (i) early in cycle, net forces are directed inward (collapse failure) (ii) late in cycle, net forces are balanced but sudden depressurization with high clad temperatures (LOCA) create outward forces (burst failure) (3) Thin enough to minimize temperature drop (4) Thin enough to promote good neutron economy Resulting Values of Clad Thickness PWR:.5-4 mils BWR: 6-3 mils
Determination of uel Height The maximum linear heat rate is related to the core thermal power by q max Q f nh q or a given core thermal output and nh that satisfy this relationship What determines H? q max, there are an infinite number of combinations of Desirable Properties: (1) Neutron economy: or a fixed critical Buckling, minimum core volume occurs if H D eff 0.9 () uel costs are reduced if the number of fuel rods and assembly units fabricated is minimized. SOLUTION: a) ix core height allowing a standard fuel assembly to be fabricated. b) Increase plant power rating by increasing the number of assemblies (simplifies T/H design considerably). c) Select a value of H, such that (H/Deff) is acceptable over a fixed range of plant power ratings. Compromise: H = 1 ft. and (H/Deff) has a range of acceptable values depending on plant power rating. H 0.9 1.5 D eff
Define an effective core diameter Deff, such that D 4 eff A core The core area is constructed from an integer number of Assemblies A ( N ) N N S core assemblies assemblies array S Nassemblies Narray D o D Set by CH o Set by neutronics D eff ( N ) assemblies 4 A ( N ) core assemblies or a target H D eff H( N ) D ( N ) assemblies eff assemblies The number of fuel rods is also a function of the number of assemblies nn ( ) N ( N N ) assemblies assemblies array H O q max f nn ( ) HN ( ) assemblies Q q assemblies Which can be solved for Nassemblies H
X-Sectional Area for Coolant low Since fuel rod size is fixed by constraints previously discussed, specifying the water/fuel (Pitch/Diameter) ratio uniquely fixes the X-sectional area for coolant flow. But as we shall discuss in ND section, water/fuel ratio is bounded on the lower side by the need for sufficient moderation (economics fuel cycle cost) and on the upper side by the safety constraint that a moderator (coolant) density decrease must result in a negative addition of reactivity. Conclusion: There is a limited range of (water/fuel) ratios dictated by neutronics. Core Inlet/Outlet Temperatures and Mass low Rate How does a T/H designer choose coolant inlet and outlet temperature and mass flow rate (PWR only since pressure fixes outlet temperature for a BWR)? The core temperature rise and coolant mass flux are inter-dependent Total Power: HO Q C T GA RX p core flow m HO T T T HO core out in (coolant temperature rise) # G = coolant mass flux hr ft =X-sectional area for HO flow A flow Desirable Coolant System Characteristics (1) Mass flow rate (A) large G desirable to provide margin to CH (B) low G desirable to minimize lift forces, jetting and pumping costs () T HO out core outlet temperature HO (A) High T desirable to maximize plant efficiency and/or reduce capital costs out Q Q U A T PWR S/G: RX SG SG SG M
T T ( T, T, T ) m m HL CL SG, => ASG HO T T T out HL m ASG THL TSG SG or smaller steam generator size. (and P ) increasing thermal efficiency. (3) (B) low T HO out desirable to provide margin to CH (C) low T HO out desirable to avoid crud deposition on fuel rods and resulting corrosion problems HO T core inlet temperature in (A) high (B) low HO T desirable to minimize steam generator size and/or increase steam pressure in HO T desirable to provide margin to CH in T/H Design Compromise: (1) Choose T HO out (averaged over core) such that voiding in hot channel is as high as allowable => dictated by maximum primary loop pressure (PWR design restricts amount of voiding allowed during normal operation). Also impose crud deposition limit (oxidation of clad sets current limit). () Assuming (water/fuel) ratio is fixed from neutronic considerations, total power output calls for T core G to have a unique value. This in turn implies specifying T HO in fixes G. One now evaluates the highest T HO in (and associated G) that provides appropriate margin to the CH.
Typical Behavior for a PWR H T O o in about 5 o 0 % Power 100 PWR BWR HO T in T HO out 560 o (@ ull Power) 65 o (@ ull Power) 530 o 550 o (sat.) low 1.4x10 8 #/hr 1.1x10 8 #/hr
Representative PWR Primary Coolant Temperatures as a unction of Power
Core (Height/Diameter) Ratio (Affect on T/H Design) Assembly low Area D o S NArray S NArray D o 4 4 fixed D o fixed Core low Area D o S Aflow Nassemblies NArray S Nassemblies NArray D o 4 4 fixed D o fixed or HO Q C T GA RX p core flow m Change (H/Deff) => Change Nassemblies => Change Aflow => Change G for specified (ΔT)core
Additional Points (A) It should be noted that only about 97.5% of the fission energy is deposited in the fuel, which contributes to the surface heat flux. About.5% of the fission energy is in the form of neutron kinetic energy, which is deposited directly in the moderator during thermalization. (B) Grids are usually designed to have mixing vanes, which promotes turbulence and increases the CH. ND information about the power distribution is needed by the T/H designer to determine a design which does not exceed rod thermal limits. The most important power constraints can be summarized as: PWR: (1) Total core peaking factor q = Peak Power Density / Average Power Density (a) During normal operation sets core average kw/ft based on LOCA limit (b) During accidents sets overpower protection system trip function to preclude fuel damage via centerline melt and other non-ch mechanisms () Axial peaking factor (peak to average ratio) or q( z) q 0Z( z) qz ( z ) Z( z ) 1 1 qzzdz ( ) Zzdz ( ) H 0 max max z H H 0 0 H 0 (3) Most limiting axial power shapes from a CH ratio viewpoint (4) Enthalpy peaking factor H R as a function of power level / q H z H q z R / H q z = Highest powered rod in the core/average rod power Items () through (4) are used to evaluate whether the CH ratio limits are violated, with specified minimum values for normal operation and accidents.
Typical Allowed ΔH Values During Normal Operation for a PWR H 1.75 1.55 *Goes up with decreasing power since more CH margin 0 % Power 100 BWR: (1) Maximum raction of Limiting Power Density = Power Density for Pellet " k " max k Limiting Power Density for Pellet " k " Originates due to clad strain limit. () Maximum raction of Limiting Average Planar Linear Heat Generation Rate = Power Density for Bundle " j" at elevation z max jz, Limiting Power Density for Bundle " j" at elevation z Originates due to LOCA limit. (3) Minimum raction of Limiting Critical Power Ratio = Limiting Critical Power Ratio for Bundle " j" min j Critical Power Ratio for Bundle " j" Critical Power Ratio = Core power level that causes dryout/operating Power for a fixed power distribution and coolant inlet conditions.