Drift-Flux Model Nonlinear Dynamics and Chaos

Abstract

After analyzing the linear stability of the Drift-Flux Model for boiling channels, in this chapter we address the question of the nonlinear evolution of density waves after their initial growth. In particular, we are interested in the occurrence of sustained oscillations under operating conditions close to the linear stability margins.

First, a nonlinear discrete mapping derived with the Drift-Flux Model with transport delays is used to get a preliminary understanding of the development of stable and unstable limit cycles at high and low N _SUB numbers, respectively. With this simple model it is possible to visualize the effect of the drift velocity, V _gj, on the limit cycles.

Then, the Moving Nodes Model (MNM), which was originally developed for homogeneous two-phase flow (DiMarco et al., International Journal of Heat and Technology 8: 125–141, 1990; Clausse and Lahey, Proceedings of the 9th International Heat Transfer Conference, Jerusalem, 1990; Chaos, Solitons & Fractals 1:167–178, 1991) and was applied extensively, particularly in the nuclear industry, is extended to incorporate drift flux. The MNM is applied to simulate and analyze the nonlinear dynamics of a system comprised of a boiling channel coupled with an adiabatic riser, which is relevant to recent advanced water-cooled nuclear reactor designs, among other applications. A complex nonlinear dynamic behavior is encountered at operating conditions of incipient boiling at high N _SUB. The flow reaches sustained chaotic oscillations alternating with limit cycles of different periods and quasi-periodic oscillations.