The fuel rod behavior caused by irradiation of fuel pellets and cladding is complicated for investigation in an analytical method. Fuel rod behavior calculation codes were developed from various experiments and operational experiences. FEMAXI-6 [30] as an open code developed in Japan is a general analysis code for fuel rod behavior at normal operation or abnormal transients in LWRs. It constructs a model composed of one fuel pellet, cladding, and internal gas, and then analyzes thermal, mechanical, and chemical behavior and reciprocal action at normal operation or abnormal transients from overall power history data. Table 2.3 shows fuel rod behavior analyzed in FEMAXI-6.

The overall structure of FEMAXI-6 consists of two parts, thermal analysis and mechanical analysis, as shown in Fig. 2.49. The thermal analysis part evaluates radial and axial temperature distributions considering a change in gap size between pellet and cladding, FP gas release models, axial gas flow and

res

Output

Fig. 2.49 Overview of FEMAXI-6 structure

its feedback to heat transfer in gap, and so on. The mechanical analysis part applies the finite element method (FEM) to the whole fuel rod and analyzes mechanical behavior of fuel pellet and cladding as well as PCMI. It also calculates an initial deformation due to thermal expansion, fuel densification, swelling, and pellet relocation, and then calculates stress and deformation of pellet and cladding considering cracking, elasticity/plasticity, and pellet creep. The thermal and mechanical analysis is iteratively performed to consider the thermal feedback effect on the fuel rod mechanical behavior. Further, the local PCMI can be analyzed by the 2D FEM, based on the calculation results from both analysis parts such as temperature distribution and internal pressure.

Figure 2.50 describes the calculation model of FEMAXI-6. The entire fuel rod is divided axially into several tens of segments and radially into ring elements. For example, the figure shows ten axial and radial divisions in the fuel pellet.

Fig. 2.50 FEMAXI-6 calculation model

FEMAXI-6 contains various calculation models and experimental correla­tions that users can specify. Details of models, physical properties, or correla­tions are described in the code manual [30] of FEMAXI-6.

Exercises of Chapter 2

[1] Consider a PWR UO2 pellet 0.81 cm in diameter, 1.0 cm in height, and 10.4 g/cm3 in density in which the uranium is enriched to 3.2 wt. % 235U. Answer the following questions.

(a) Calculate the atomic number densities of 235U, 238U, and O in the pellet.

235 238

UO2 contains only U, U, and O. Their atomic masses are M (235U) = 235.04, M(238U) = 238.05, and M(O) = 16.0, and Avogadro’s number is 0.6022 x 1024.

(b) One-group microscopic cross sections of 235U, 238U, and O are given in the following table.

Nuclide	Absorption ca (barn)	Fission cf (barn)
235U	50	41
238U	1.00	0.10
O	0.0025	0.00
(1 barn =	= 10-24 cm2)

Compute the macroscopic absorption and fission cross sections of the pellet. What is the probability that a neutron will cause a fission on being absorbed into the pellet?

(c) Compute the mass (in tons) of metal uranium in one pellet 1.0 cm in height. A PWR fuel assembly consists of 265 fuel rods bundled into a 17 x 17 array (including 24 guide tubes) with an active height of 366 cm. Compute the initial mass of uranium in one fuel assembly and compute the total loading amount of uranium (the mass of metal uranium) in the core which contains the 193 fuel assemblies.

(d) Calculate the linear power density (W/cm) of the fuel rod when one-group neutron flux in the pellet is 3.2 x 1014 n/cm2-s. The energy released per fission is 200 MeV (1 MeV = 1.602 x 10_13 J). What is the specific power [power per initial mass of metal uranium (MW/ton)]?

(e) Compute the burnup (MWd/ton) of the pellet consumed along the specific powers as shown in the figure

				38.0
36.0
c	)verhar	il (	s 15 CD >	1
^ 285 Days ^		^ 290 Days ^		^ 280 Days ^

CD £ c£

<D ft m

41.0

Time [Days]

(f) Compute the consumed amount of 235U in the pellet from the burnup of (e). Two-thirds of the total power is generated by the uranium ( U and U) fission and the rest by the fission of plutonium produced from the conver­sion of 238U.

[2]

An infinite slab of non-multiplying uniform medium of thickness d (= 400 cm) contains a uniformly distributed neutron source S0 as shown in the following figure.

The neutron flux distribution in the slab can be determined by solving the one-group diffusion equation

d[7](b(x) , x

D +Xa0 (x)=So

where D = 1.0 cm, 2a = 2.5 x10-4 cm-1, and S0 = 1.0 x 10-3 n/cm2-s. Discretize one side to the reflective boundary in the middle into four meshes (N = 4) and calculate the neutron flux distribution using the finite difference method. Plot the distribution and compare it with the analytical solution

SQ( cosh ф ____

ф(х) — — 1—————— j— where, L = y/D/I. a

Л

Calculate for N = 8 and 16 if programming is available.

[3] (a) Consider a multiplying system with an effective multiplication factor kf. Develop the diffusion equations for fast and thermal groups in terms of the two-group constant symbols in the following table.

Fast	group			Thermal	group
X1	1.00			/X 2	0.00
V1	2.55			V2	2.44
2,1	2.76	x	10-3	2,2	5.45 x	10-2
2a, 1	9.89	x	10-3	2a, 2	X О <N oo	10-2
21!	2 1.97	x	10-2	22!1	0.00
D1	1.42			D2	0.483

(b) Calculate the infinite multiplication factor k^ using the two-group constants.

[4] The burnup chain of 135I and 135Xe is given by the following figure

Show that the equilibrium concentration of 135Xe (NXe) in the reactor operating at a sufficiently high neutron flux is given approximately by

jr+rp^f

,-rXe О a

where уI and yXe are the fission yields of 135I and 135Xe respectively, and ^Xe is the one-group microscopic absorption cross section of 135Xe and Lf is the one-group macroscopic fission cross section.

[5] The energy conservation equation is given by Eq. (2.117) for no water moder­ation rod. Develop the energy conservation equation when introducing the water moderation rod.

[6] Develop equations for single-phase transient analysis at the 1D axial node i of a single coolant channel, based on the mass conservation equation [Eq. (2.116)], the energy conservation equation [Eq. (2.117)], the momentum conservation equation [Eq. (2.118)], and the state equation [Eq. (2.119)], referring to the figure.