To compare to the prediction of the first and second roots (instability lines) at low and high quality there are many data in the literature. We must know, or be able to estimate or calculate the loss coefficients and use only data where the channel pressure drop is constant, relevant to the reactor situation.

Definitions for the experimental onset of instability are not universal, and were often reported as the onset of density wave oscillations, not static instability, obtained by usually raising the power until some unstable or oscillating flow was observed. Data review yielded over 300 data points, extracted from 30 years of the literature, covering a range of pressures from 0.1 to 19 MPa,(i. e. nearly 1-190 bars), for tubes, rod bundles and parallel channels. In Figure 3, the data and theory are shown, with the density wave data cluster at the lower subcoolings and powers.

FIG. 2. Typical stability maps for different flow directions.

World Data and Theory Limits FIG. 3. Comparison of data and stability theory showing stability and CHF boundaries.

In non-dimensional Np versus Ns space, the data clearly map out a central unstable (uninhabited) region. The best fit through the lower limit of the saturated data is given by a line of slope (Np /Ns) = 3), which is the asymptotic limit of Equation (8).

From this form of plot we see that stability is possible when operating in the high Np and lower Ns region, and the first and second unstable lines are given by,

Np /Ns = N* (13)

For the second characteristic line at high quality, we have N* is O(3), from both theory and experiment: for the first characteristic line in the low quality subcooled region, stability is possible when N* is 0(1).

Now, in a natural circulation loop with n channels, we define the region of instability as given by the intersection of the unstable region from the instability with the natural circulation flow. We find that we can maintain stable natural-circulation flow below the critical subcooling number. However, for larger subcooling, the natural-circulation line is in an unstable region and therefore, flow will be unstable. Basically, the downcomer level should be maintained high enough to have imposed pressure higher than the high-void-region extreme of the pressure drop-flow curve.

The intersection of the natural circulation flow with the unstable region for larger downcomer heights (L* ~ 0.3) is at a value of Np/Ns of about 2, which implies the maximum stable power level for the system is close to the theoretical and experimental stability limit. For lower downcomer heights, L* ~ 0.5, the intersection is closer to the minimum value of the unstable region. Thus, we also have the analytical result which determines the instability boundary and the onset of CHF in a natural circulation system.