It is important to note that stability limits in natural circulation systems arise before (and as a prelude to) CHF or DNB. Indeed, conventional forced flow CHF and DNB correlations cannot be applied to natural circulation and parallel channel systems if either the loss coefficients are unknown or not reported, or the appropriate constant pressure drop was not maintained or achieved in the tests. Throttling the inlet flow to set a flow boundary condition artificially stabilizes the channel. In actual plants, it is well known that the plant maintains a constant pressure drop, by having multiple parallel channels and/or a controlled downcomer hydrostatic head.

Designs of pressurized systems limit the heat removal to that determined when there is no bulk boiling. The flow is always subcooled, and the heat exchange is by single-phase (liquid) flow in the heat exchanger. Heat removal in normal and accident conditions can be set by the convective heat removal by natural circulation.

We would like to establish the maximum or ultimate heat removal in a natural circulation design where there is a known elevation difference between the heat source (core) and sink (HX). The maximum power limit is when the heat generated is completely removed by the heat exchanger loop, and the HX outlet temperature is close or equal to the secondary side (boiling) temperature. The turbine stop valve (design) pressure of course sets the secondary

side temperature. Thus, there is a relation between the core maximum (saturation or subcooled) temperature, and hence the power, and the secondary pressure.

For the purposes of the maximum design output evaluation, we define the maximum core outlet temperature as the saturation temperature at the primary pressure. Thus the ultimate limit is taken as bulk boiling at the core exit and not conventional DNB. We consider the two — phase (boiling) limit later and use results available from the literature (Duffey and Sursock, 1987); (Duffey and Rohatgi, 1996).

The overall loop flow W, in a natural-circulation system with a thermally expandable fluid, utilizing the Boussinesq approximation, Ap= pfiAT, for the expansion coefficient, Д is given by the well-known result

Here A is the flow area, K the loop loss coefficient, AZ the effective available driving head between the heat source and sink, Q the power, g acceleration due to gravity, pe the liquid density and cp the heat capacity.

Since the two — phase flow rate W24> in the loop is given very nearly by:

or

1/3

‘P

q 2 hg b fgH

where Ф = pt/(pt — pg) and hfg is the latent heat and Cp /hfgb is a dimensionless evaporation number.

Thus we expect to find that most major loop and system parameters have a relatively weak (one-third power) influence on the flowrate.