Chaotic attractor in a periodically forced two-phase flow system

Motivated by the enhancement of heat transfer under oscillating flow conditions in single-phase heated channels and by stability problems in two-phase systems such as those in boiling water reactors, density-wave oscillations have been analyzed by numerically solving the nonlinear, variable delay, functional, ordinary integrodifferential equations that result from integrating the nonlinear partial differential equations for the single- and two-phase heated channel regions along characteristics and along channel length for axially uniform heat fluxes. The cases of constant pressure drop ΔP_ex across the channel (steady-state feed pump operation), exponentially decaying ΔP_ex (feed pump coastdown), and periodic ΔP_ex (feed pump oscillations) were studied. The nature of the strange attractor was analyzed quantitatively by calculating its correlation dimension - an estimate of its fractal dimension - and the dimension of the phase space in which it can be embedded. These calculations indicate that the change attractor is indeed a fractal object of fractional dimension 2.048±0.003 and embedding dimension 6.