It is assumed now that no molten fuel is present. The problem is whether, following the cladding rupture, the release of fission gases might blanket

and insulate an adjacent pin and cause a secondary failure. The results quoted below all refer to fuel pins of 0.2-0.25-in. diameter in a pitch-to — diameter ratio of about 1.25. The case is a very important one because the event of a failure of a high burn-up pin is a likely fault by the very statisti­cal nature of the fuel and cladding fabrication process. Indeed plants have been designed to run with some failed fuel.

What experimental evidence there is suggests that no damage results subsequent to the first failure. The Soviet BR-5 was deliberately run at higher then design burn-ups for some considerable time and despite a significant number of failures, no report of any propagation mechanism was discovered (18).

Table 4.4 outlines results obtained in the USA for a 19-rod bundle (6 ft by 0.24 in. diameter with a 50-mil wire wrap on a 12-in. pitch) in which gas was released through different sized holes at different flow rates. Photo­graphic records of the experiment, staged in water, showed that for large hole sizes, the outgoing gases could cause the channel flow to reverse but only for a very short time. Smaller hole sizes sustaining a longer outflow of gas caused no reversal and no coherent channel bubble but merely a stream of bubbles (19, 20).

Table 4.4 also outlines other work for a 7-pin bundle in water (21). Air was released through holes of varying sizes at various pressures into the coolant flowing with a coolant velocity of 20 ft/sec. The coolant pressure was 30 psi. No reversal was observed in the coolant flow, although measure­ments of flow against the opposite pin showed regions where the effective flow was reduced to as little as 5% and very small regions where the flow was zero.

Analytically, the consequences of fission-gas release within a coolant channel may be bracketed between large and small flow rates and their different consequences. First the rate of emission of gas may be calculated for a given rupture, depending on the pressure differential between the fuel — pin fission-gas plenum and the external pressure in the channel, if one knows the pressure drops along the path through the fuel by which the fission gases emerge (19).

Figure 4.15 shows a cross section of the fuel and the sintered and un-

sintered regions. Also shown is a postulated path for the flow of fission gas from the plenum through cracks in the outer region, through inter­connected pores in the inner zone to the central void and a reverse path through the sintered and unsintered zones to the rupture of the cladding. Digital codes (see Appendix) exist to calculate flow rates through this tortuous path based on estimates of pressure drops that might be expected. The calculation takes into account the fact that the fission gas exits at sonic velocity, as long as the pressure ratio across the cladding rupture is greater than about 2 and thereafter the release is subsonic. Thus the gas outflow is calculated for different hole sizes, for different locations of the rupture, and for different assumptions of the condition of cracking in the fuel which determine the pressure drops through the fuel.

Fission gas outflows can last anything between a few milliseconds for large holes to even minutes for very small holes. Subsequent channel flows depend critically upon whether the flow rates are large or small as Table 4.4 shows; therefore, the analysis is separated into these cases.

(a) Large gas flow rates (Fig. 4.15). Based on a momentum balance, the flow rate in the channel can be shown to decrease rapidly when the fission gas enters, but it then recovers as the fission gas is swept out of the channel, until the flow regains its original value. This reducing and recover­ing flow transient can be input to a thermal assessment code to calculate the transient effect on the cladding temperature for neighboring pins. Even in the most pessimistic cases, the outflow of gas is too rapid to cause more than a moderate rise in neighboring cladding temperatures.

(b) Moderate gas flow rates. In these cases no flow reversal is assumed but it is supposed that the flow rates are large enough to allow a jet of gas to impinge upon and blanket an opposite fuel pin. Other results show that this can occur for a certain critical range of rupture sizes: between 0.005 and 0.07 in. in diameter (21).

A three-dimensional code TOSS (see Appendix) used to calculate the heat transfer for a pin that is effectively insulated for an angle 6 of its cir­cumference shows that the cladding temperature beneath the point of insula­tion rises to a level which depends on 6 (Fig. 4.16a). As Section 4.2.2.2 showed, this level is much higher for coverages of larger than about 90°.

The cladding will attain failure temperature (5b) if the insulating or heat­ing impingement of fission gas remains in situ for a long enough time (te) which varies with the angle of coverage 6°. The value of te will depend on the characteristics of the jet and its possible deflection by the stream (19).

The following empirical equation can be used to represent the jet deflec-

tion (velocity in feet per second and dimensions in inches):

x/d0 = (2.02 ?g Kg2/ec Ус2) log [1 + (0.049y/d0)] (4.31 a)

where x is the penetration into the mainstream, у is the downstream de­flection in a channel of diameter d0, and gg, Vg, gc, VB are the density and velocity of the gas and coolant, respectively. The deflection у varies with time as the gas velocity decreases through the rupture and te is the total time that a point on the adjacent cladding has been blanketed by the jet of gas. The jet also disperses in the flow according to the equation

jet width h = 2.25r/0 + 0.22x (4.31b)

and this jet width will define 0, although of course the jet will also tend to smear around the adjacent pin thus increasing the effective blanketing coverage.

Thus failure can only occur by this mechanism if the cladding rupture is such as to produce a blanketing of the opposite pin of 6° for a time long enough to achieve failure temperatures te. This demands that the rupture size be large enough to give a reasonable coverage, since smaller holes will give a smaller gas flow rate and therefore the jet may be deflected too greatly by the stream. On the other hand the rupture size must be small enough to sustain a gas jet for a time greater than t0. Thus there is a critical range of rupture sizes which might cause an adjacent failure.

Recent calculations (19) report that this critical range is between 10~4 and 10-5 in.2 in area.

Even within this critical range, there is yet no hint of the possibility of a continuing failure, for if a second failure is produced, it will still be direc­ted back toward the original ruptured pin. In order to produce a chain of failures the second pin would have to also fail with a rupture size within this same critical range and at the same time be directed toward a third pin. This does not seem likely.

(c) Low gas flow rates. If the gas flow rates are very low then they will be sustained from small holes or locations distant from the fuel fission gas plenum for several minutes. The conditions in the channel are now two — phase and the analysis of Section 4.2.2.1 can be used to compute the effect on neighboring pins. This effect has been seen to be small for even void fractions approaching 50%.

Thus by separating the analysis into three distinct flow regimes, it has been possible to calculate temperature changes in the cladding of the neighboring fuel pins to determine whether any subsequent failure is caused that might lead to propagation of the original failure. The three analytical regimes are not strictly defined, they overlap although it appears that with internal fission pressures of 800-1000 psia the gas cannot cause a flow reversal for hole sizes greater than 0.06 in. in diameter at these flow rates (20).

The results lead to the following conclusions:

(a) For single failures the most critical size of rupture appears to be in the neighborhood of 0.01 in. in diameter (10~4-10-5 in.2 in area) when a jet can be sustained to blanket the opposite fuel pin.

(b) For single failures, the most critical rupture location is at the middle of the fuel pin; ruptures nearer the plenum release the gas too rapidly and ruptures further away do not provide a very large flow volume rate.

(c) Even at these most critical conditions, temperature rises in the clad­ding of the adjacent pins are limited to very local positions, so that if a failure occurred in an adjacent pin, then the failure would be directed back toward the original failure. Thus it is most unlikely that this failure could propagate. Experience to date certainly substantiates this position.

Although once a problematic condition, it appears that experience and analysis have shown that a failure which releases only fission gas does not propagate. Because of this, experimentation on this condition is now being brought to a close.