INFLUENCE OF NUCLEAR HEATING ON 2-PHASE CHANNEL INSTABILITIES

Non-linear density-wave instabilities are analyzed for two-phase channel flows with nuclear heating. The fluid is homogeneous and enters the channel at saturated conditions. A Lagrangian formulation is used to re-express the governing equations as an integro-differential system. Asymptotic analyses, based on multiple-scale expansions, are exployed to determine the evolution of velocity perturbations arising in the neighborhood of the linear stability boundary. This region is governed by a Landau equation and the relevant constants are evaluated. Over much of the system parameter space supercritical perturbations evolve into limit cycles, and subcritical disturbances decay with time. Increasing the magnitude of the channel power or the void reactivity coefficient does, however, lead to a transition in the channel response. Within this regime supercritical disturbances grow into large-amplitude instabilities. Provided that the initial amplitude exceeds a certain threshold value, subcritical perturbations also develop finite-time singularities. Except in a very narrow region dose to the neutral curve, calculations show that this value far exceeds practical fluctuation amplitudes. Numerical simulations of the non-linear channel dynamics are carried out by a method-of-lines technique. Although perturbations arising near the neutral curve evolve on time scales considerably longer than the basic scale associated with the oscillatory behavior, the numerical technique yields results that agree closely with the asymptotic theory.