tage of developing a UO» fuel that has 
a high value of the integral 
max. fuel temp. 
i ae temp. 
where k(@) is the thermal conductivity 
and is a function of the temperature, 0. 
This expression is very useful in fuel 
design (58) to compare the irradiation 
behavior of specimens of similar surface 
temperatures but of differing diameter, 
enrichment, density, heat rating and 
fabrication history. It can be applied 
without information on thermal con- 
ductivity and its variation with tem- 
perature and irradiation, the tempera- 
tures at which grain growth and melting 
occur or the type of sheathing used. 
The integral can be obtained as a 
product of two terms, one determined 
by the measured heat-transfer rate and 
the other a calculated function of the 
specimen’s properties, e.g. 
k(@) dé 
Tr 
7, (0) a6 = ue - fn(xca,r) 
= (q/4m) - fn(xa,r) 
where 
Io(xa) — T(r) 
=9 
fn(xa,r) xa + 1\(xa) 
which has the value unity at r = 0 for 
negligible flux depression, hence uni- 
form heat generation; k(@) = thermal 
conductivity of UO, at temperature 
6, T, = temperature at radius 7, 7’; = 
temperature at UO: surface, H = 
sheath-coolant surface heat flux, R = 
radius of outside of sheath, a = radius 
of UOs, q = heat production per unit 
length of fuel, J) = modified Bessel 
function of zero order, J; = modified 
Bessel function of first order and x = 
reciprocal of effective diffusion length 
in UOz. 
Morison (60) has expressed the de- 
pendence of fn(xa,r) at r = 0 on UOz 
diameter and enrichment for 95% 
dense, solid oxide cylinders in the con- 
venient form shown in Fig. 4. Thus, 
the computation of the integral has 
been much simplified. 
According to Robertson et al. (58) 
and more recent tests on sintered ADU- 
type UO», cylindrical stoichiometric 
specimens, whose oxide surface tem- 
perature is about 400° C during irradi- 
ation, exhibit grain growth when 
center 
| ae k(6) d@ exceeds 29 + 3 w/cm. 
Rod-shaped elements irradiated in 
pressurized-water loops at Chalk River 
have exhibited completely satisfactory 
64 
performance at ratings as high as 50 
w/em. A cross section of such a rod 
is shown in Fig. 5. Central melting 
would be expected at 55 w/cm. 
It was considered useful to plot sev- 
eral irradiation results so that values of 
the integral producing grain growth 
and melting could be predicted for solid 
stoichiometric cylinders with different 
surface temperatures. This has been 
iT 
nie k(@) d@ versus 
T, a particular temperature in the fuel, 
asin Fig.6. For any given irradiation, 
T 
the value of ie k(0) dé is the differ- 
ence in ordinates for two points defined 
by the temperature limits, 7’, and T. 
The point on Fig. 6 for Pellet Rod III 
was determined by measuring the cen- 
tral temperature with a thermocouple 
and by calculating the integral from a 
knowledge of the neutron flux, hence 
the heat output from the rod. 
In plotting the points for the Cana- 
dian specimens showing grain growth 
(CR-V-e, X-2-O, X-2-g and Pellet Rod 
II), values for the integral from the ox- 
ide surface to the observed radius of 
grain growth were determined by a 
done by plotting 
80 
* 70 
60 
& 
o 
~ 
= 50 
D> 
oO 
® 
= 4 
Ro 
Pellet Rod I 
| 
1,200 
= 
method similar to that detailed in a 
following paragraph. It was assumed 
that discernible grain growth would be 
produced in the ADU-type UO» at a 
temperature of 1,500° C (58). When 
no grain growth was discernible in the 
center of an element for comparison 
with the undisturbed outer area, a 
minor change in appearance was diffi- 
cult to detect under the microscope 
used. Hence, the center temperature 
of specimens from CR-V-b and X-2-n, 
where no grain growth was observed, 
may have been as high as 1,600° C. 
The WAPD specimens 25-2-L2 and 
X-1-g5, which also showed no grain 
growth, were made from the less reac- 
tive PWR-grade UOz. Thus, a some- 
what higher temperature limit, 1,700° 
C, has Specimens 
X-1-f5 and X-1-g3 showed grain growth 
corresponding to 2,300° C at the maxi- 
mum-flux positions (57). 
The heat outputs from specimens ir- 
radiated in the CR-V and X-2 loops 
were measured calorimetrically, and 
some were checked by mass-spectro- 
metric analyses to determine burnup. 
Published heat fluxes for the WAPD 
been assumed. 
Hydraulic- 
rabbit 
melting 
Pellet Rod I 
X-2-n 
t 
2800 
\ 
2000 
Fuel Temperature (°C) 
data (57). 
FIG. 6. Summary of irradiation tests on UO» [O—Chalk River data; 0—WAPD 
Solid curves A, B, C and D are values for thermal conductivity of UO», 
4 
corrected to 95% density, taken from references 28, 30, 31 and 32, respectively; 
dashed lines are extrapolations to 2,800° C 
