9.172. With the increasing availability of digital computers for engi­neering calculations, methods have been developed for the treatment of core design limits in PWRs that are more realistic than the basic hot-channel concept described in previous sections. Rather than identify a single hot channel as representing the “worst case,” it is possible to analyze each channel individually and to determine the corresponding minimum DNBR and other limiting parameters. Statistical methods are then used to evaluate the number of fuel rods that may have a given small probability of failure, as a function of design and operating conditions.

9.173. In one example of the statistical core design technique [23], a radial power factor (ratio of actual to average), analogous to F%H, is com­puted for each rod in the core, and so also is an axial factor, equivalent to F; for each rod. Engineering factors, which are sometimes called “hot — channel” factors although they do not refer to a specific hot channel, are used to describe deviations from nominal (or design) values in physical characteristics of the fuel material, fuel pellet and cladding dimensions, and flow area. These factors are derived from several subfactors based on measurements made on the actual core under construction, on similar cores previously constructed, or on specified manufacturing tolerances. The subfactors are then combined statistically to yield a heat-input factor Fe, a local hot-channel heat flux factor F0», and a flow-area reduction factor Fa. Typical values of these engineering factors in a large PWR are as follows:

Heat input (or power peaking) factor FQ 1.011

Local heat flux factor FQ„ 1.014

Flow-area reduction factor FA 0.98 (interior)

0.97 (periphery)

9.174. The computations are made for several different operating con­ditions but two are of special interest, namely, maximum and average (or most probable) design conditions. For the maximum design condition, the maximum values of the radial and axial power factors are assumed to be applicable to each fuel rod in the core; the computed heat input (or heat flux) for each rod is then multiplied by the factors FQ and FQ>, both of which are greater than unity. The coolant-flow rate is determined using the Factor Fa, which is less than unity. In a particular case, the maximum radial factor was 1.78 and the maximum axial factor was 1.70; hence, with the engineering factors given above, the maximum-to-average heat flux ratio for each coolant channel is

Heat flux factor = 1.78 x 1.70 x 1.011 x 1.014 = 3.10.

In evaluating the coolant enthalpy rise, the factor includes an allowance for the reduction in the flow area which applies to all the channels; thus,

Enthalpy factor = 1.78 x 1.011 x 1.014 x 0.98 = 1.79.

By means of these data, it is possible to compute the DNB flux (and DNBR) along each fuel rod (or channel) instead of a single hot channel in the earlier treatment.

9.175. For the average (or most probable) design condition, the heat input (or power) distribution for each fuel rod is derived from neutronic calculations, and the coolant-flow rate is compatible with the location of each channel in the reactor core. The DNB data are then evaluated for each fuel rod (or coolant channel) in the usual manner.

9.176. The results obtained from the foregoing computations are treated statistically to derive the number of possible burnouts at a specified con­fidence level for various operating conditions. Table 9.4 gives the values obtained at a 99 percent confidence level for both maximum and most probable design conditions of a PWR with 36,816 rods operating at 100 percent of design power and at 112 percent overpower. It is seen that, under the worst conditions that might arise in normal operation, i. e., at maximum design conditions and 112 percent overpower, there is a 99 percent confidence that almost 99.9 percent of the fuel rods will be pro­tected from burnout. The minimum DNBR under these conditions is 1.39 at the same confidence level.