Nuclear Fuel Engineering (2. Modeling) Department of Nuclear Eng. KHU Kwnagheon Park

Transcription

1 Nuclear Fuel Engineering (2. Modeling) Department of Nuclear Eng. KHU Kwnagheon Park

2 2. Behaviors of Pellet during Normal Operation 2

3 2.1. Temperature Distribution in a Fuel Rod C p T t kt q ''' ( r) Macroscopic cross-section Tc ''' q ( r) Ed 0 ( E) ( re) de f 1 Ts Ti To flux ''' In Steady state, kt q ( r) 0 r Ts T f ''' In cylindrical geometry and q const. R 1 d dt ''' kr r dr q dr 0 T Ts k( T ) dt ''' q 4 ( r 2 R 2 )

4 Tc Ts k( T ) dt ''' q R 4 2 P L 4, P L = Linear Power (watt/cm) k ( t) dt If k = const. P L 4 T Ts Tc Ts r 1 R 2 Ts Tc 4

5 Thermal conductivity of Urania Pellet UO 2 Simfuel 5

6 k ( t) dt 6

7 Tc Ts Ti To q Tc Ts Ts Ti Ti To R q 1 1 d 4k 2Rh 2k R ' 2 ''' f f c R d T f Tc / T q R cf ) V I R Ts Ti To R 1 R 2 q / R R k f R 2 1 2Rh R d 2k c R 7

8 Heat transfer coefficient in the gap 8

9 Temperature and Power Profile 9

10 2.2. Temperature Effects - Thermal Expansion : 10

11 - Fuel Cracking : Maximum tensile stress : Max E 2(1 ) ( T C T S ) Or, T C T S 2(1 ) E Rupture ~ 10MPa About 100 o C difference can cause cracks. 11

12 - Thermoelastic Strain : Plane strain condition is not valid in the vicinity of the TOP, BOTTOM. Chamfer Dishing 12

13 2.. Irradiation behaviors of Pellets - Densification POROUS UO 2 GRAIN (MANY FINE PORES REPRESENTED BY ONE CIRCULAR PORE AT THE CENTER OF A GRAIN) HOMOGENIZATION BY FISSION FRAGMENTS (ARROWS) DISPERSE THE PORE AS VACANCIES ( MARKS) DENSIFICATIION OF ORIGINALLY POROUS GRAIN BY ELIMINATION OF VACANCIES AT EXTERNAL GRAIN SURFACES DIFFUSION OF VACANCIES FROM POINTS OF HIGH CONCENTRATION TO GRAIN BOUNDARIES. 1

14 14

15 As fabricated UO 2 has a bimodal pore-size distribution. Properties Fine Pores Coarse Pores Initial Population Porosity Mode of Interaction with fission products R ~ 0.1 μm N : large P < 1% Complete destruction if in path of spike R ~ 0.6 μm N ~ cm - P ~ 5% Loss of 10 4 vacancies from pore at each spike Behavior of vacancies generated by encounter with fission fragment Contribution to densification Either trapped by coarse pores or by grain boundaries Rapid and complete Retrapping by pores or migration to grain boundaries Slow; maybe never complete 15

16 If rate controlled by the resolution process(pore density unchanged) : Let b : probability/sec of ejecting a vacancy from a pore to fuel matrix q v : vacancy loss rate/pore q v d dt 4 R p 4 R p b Where R p : Pore radius, Ω : UO 2 volume Then, the porosity, P becomes ; Or, R dr p dt p R 1 br po e 1 bt p P dp dt N V p p R R p V R p ' p o V R po P dr o p Pbe o dt 2 po p po bt p o However, if resolution rate is large, the vacancy in matrix may come back to pores. 16

17 Effects of Densification in LWR s 1) Axial shrinkage appearance of gaps induces collapse of claddings. Collapsed cladding : space filled by water, extra moderator caused local neutron flux peaking and a local power spike, which may overheat fuel. 2) Radial Shrinkage If collapse occurs, ovality of cladding occurs. If no collapse, fuel overheats due to the increase in gap size Remedies for densification 1) Increase initial fuel density ; however, some internal porosity must be left to accommodate fission product swelling. 2) Microstructure control during fabrication: Large grain size. Large pore size. 17

18 Spacers ovality ; Collapse gaps 18

19 - Fuel swelling due to solid fission product Definition of Swelling : The initial volume of fuel, V 0 ; 0 V ( ) V solid fp V V V 0 0 where V v UO N 0 2 U vuo 2 is the partial volume of UO 2, 0 NU is number of U. The final volume of fuel, V ; V 2 v UO N U + v i N i solid fp, i Hence, the swelling due to solid fission products is ; V ( ) V solid fp ( solid fp, i Y i v v i UO 2 1) 19

20 Typically, V ) V ( solid fp (0.01~ 0.0) 20

21 - Fuel swelling due to fission gases Basic processes 1) Nucleation : Xe, Kr diffuse to form embryo bubble population (10 14 ~ ) small bubble per cm fuel (about 10A diameter) 2) Growth : Collect newly created gas by diffusion and grow ) Resolution : Bubbles disappears because atoms in them are driven back into by collision with fission products 4) Coalescence : Randomly migrating bubbles collide to form bigger bubbles. 5) Pinning : Dislocations and grain boundaries trap bubbles. 6) Thermal gradient migration : At high temperature, bubble starts move up to a temperature gradient 21

22 Xenon equation of state 1) Van der Waals eqn : P(V nb) = nkt where B = constant corresponding to Xe atomic volume (~85A ) R : hydrostatic stress ( compressive) P Surface energy, (tension) 22

23 Force balance in surface P R 2r Where P : pressure inside the bubble So, B kt B n V kt P g 1 Where ρ g is gas density Neglecting the hydrostatic pressure, σ : R kt B g 2 1 Where A kt The number of gas atoms in a bubble, m is : R kt B R m ) 2 ( 4 If R > ~ 500A, ideal gas limit kt R m If R > ~ 10A, dense gas limit B R m 4 2

24 Swelling due to gas bubbles Assuming N bubbles of radius R in a unit volume of fuel, the swelling due to bubble become V V 4R If the fuel contains different size of bubbles, then N V V 4 0 R N( R) dr Swelling : Fission gas balance Y xe F t = C + mn - (1) Where C = gas concentration as atoms in matrix m = number of gas atoms in a bubble N = bubble density (per cm ) 24

25 m dm R -(2) And, 4RDC bm -() kt dt Where b = resolution parameter = probability per sec that an atom in the bubble is redissolved Solve simultaneously R, m, c. In a special case where resolution is neglected and c ~ 0 : Y xe Hence,. F t mn 4 2 R kt Y Ft Xe R 4 2 N So, swelling due to fission gas bubbles become ; V V fg 2 N kt 4 kt Y Xe R N 4 2 N Where Ω = volume of UO 2 25

26 Percent volume change % TD UO 202K 98% TD UO 1928K 96% TD UO 159K 80% TD UO 166K 200K 1928K 159K 166K Fuel burnup ( fissions/m ) 26

27 - Fission Gas Release Fission yield of Xe, Kr in LWR : ~0. Athermal Process Range of a fission fragment : ~ 10 μm gap Pellet fission cladd Kr 88 release Athermal process 온도 10 μm Surface of pellet 27

28 Thermal Process : diffusion mechanism Bubble formation Interconnection of bubbles 28

29 29

30 Modeling: Equivalent sphere model A polycrystalline pellet is treated as a collection of spheres of uniform size characterized by a single equivalent radius, a: where, S T =total surface area; V= volume, S T V a C 1 C t r r r 2 yf D r C 2 Cr (,0) 0 Ca (,0) 0 Jt () yf 2 1/2 Dt Dt a f 1/2 1/2 4 J 4 Dt Dt 4 Dt 1/ /2 2 4 a 2 a a ayf 0

31 Rim region 1

32 Fuel Microstructure with Burnup 2

33 High Burnup Fuel (55,000 MWD/MTU ) Rim

34 Summary Fuel Materials : fissile, fertile, fissionable materials Temperature distribution, thermal expansion of pellets Fuel behaviors during operation - Volume change of pellet - Fission gas release - Cladding corrosion, hydriding, irradiation growth - Pellet Cladding Interaction Causes of defective fuels Properties of high burnup fuels Fuel behaviors at accidents 4