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The Stability of Boiling-Water Reactors and Loops

L. G. Neal, S. M. Zivi

Nuclear Science and Engineering

Volume 30 / Number 1 / October 1967 / Pages 25-38


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This paper describes a comparative study of analytical models for calculating the hydrodynamic stability of natural-circulation boiling systems and experimental data. The models were evaluated by comparing their physical assumptions, the mathematical simplifications, the methods of solving the equations, and, in some cases, their predicting abilities. The predicting abilities of the models were determined by programming them for a digital computer and using the program to predict experimental loop stability. The models all have many common features. Each is a statement and solution of the conservation equations for the two-phase and single-phase fluids, derived and applied using essentially the same physical assumptions. In all of the models studied, the dynamics of the instability can be described as linear feedback between flow rate and vapor volume. Although some of the models include nonlinearities in the flow-void interaction, the non-linearities are not important in determining the instability threshold, but merely affect the limit cycle oscillation. All the models contain empirical correlations for slip ratio, friction, and heat transfer derived from steady-state data. There are three major differences between the models: 1) the different slip ratio and friction assumptions or correlations, 2) the extent to which distributed parameters are spatially lumped, and 3) the use of linearized small perturbations and computation in the frequency domain, or integration of the differential equations  in time with retention of nonlinear effects. The first two differences have important effects on the accuracy of the models' predictions, whereas the third difference is a matter of convenience. The STABLE-3 program by Jones is the most reliable, and predicts the threshold of instability for loop experiments within 20% for about 70% of the tests. The model of Jahnberg is a distant second in predicting loop stability. The application of Jones' FABLE program, which includes the STABLE-3 hydrodynamics in addition to feedback from the reactor kinetics equations, to the EBWR produces a calculated instability threshold in agreement with the reported 120 MW. The important destabilizing mechanism in the EBWR arises from differences between the plate-type and the rod-bundle-type fuel assemblies in the core in their steam void response to power disturbances. These dissimilarities allow the excitation of a hydrodynamic resonance interaction between the regions with the different fuel assemblies that lowers the instability threshold.

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