Given the above description of the APEX Facility, it is an intuitive assumption that no simple flow model will be adequate to predict the transient break flow behaviors for all possible plant conditions. This assumption leads to the introduction of an integrated method that is not as sensitive to the system’s initial conditions.

Because a critical flow condition existed at the break location from the onset of the transient up to the point of ADS-1 actuation, a constant mass flux is assumed from the onset of the transient,

Also, the discharge coefficient of the break nozzle is assumed to be unity,

Using these two assumptions, the integral relationship for the total mass exiting through the break nozzle,

becomes

Now, define an inverse residence time parameter,

where is the initial mass flow rate through the break and is the total mass both above the break location and within the pressurized system. Also, the fraction of mass remaining within the system as a function of time is defined as

It is simple to derive a dimensionless group from Equations 5-4 through 5-7 in terms of time and initial conditions only:

Thus, it can be shown that

The dimensionless groups described in the previous section were used to predict the total mass exiting the primary system through the break. The analysis was performed for test times prior the actuation of the ADS for all data, but it should be noted that ADS-1, ADS-2 and ADS-3 valves were not opened during the test, NRC-5001. The BAMS break flow data was integrated and used in Equation 5-6 to determine the time-dependent value of . Then, for the same range of time, t, the values of were calculated using Equation 5-7. Table 5-1 summarizes some important information regarding the results of the aforementioned data analysis, and the data is shown in Figure 5-1 through Figure 5-7. The purpose of the linear regressions is to determine how well the integrated mass model corresponds to the measured data.

As can be seen in Table 5-1, the simple integrated mass model yields good predictions of mass losses through the break nozzle to the time of ADS-1 actuation. System conditions change significantly beyond ADS-1 actuation, thus the model would not be valid.

Using the normalizations, the data can be condensed to a single plot, and the result is shown in Figure 5-8. This result is quite astounding in that it demonstrates that a very simple flow model is capable of accurately predicting the break flow behavior of the APEX test facility to the time of ADS-1 actuation.