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. In the periodic ..delta..P/sub ex/ case (feed pump oscillations) when the system is in the linearly unstable region, it usually evolves asymptotically to one of several different attracting sets, depending on the frequency of ..delta..P/sub ex/: stable period-N limit cycles, stable invariant tori, and a chaotic (or strange) attractor. 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 strange attractor is indeed a fractal object of fractional dimension 2.048 +- 0.003 and embedding dimension 6. The results of these numerical studies suggest that the heated channel model can operate safely in the linearly unstable region in a dynamically stable mode without excessively large excursions when driven at many frequencies; however, at many other frequencies it cannot. The trajectories that do remain in bounded regions of phase space can be, depending on the forcing frequency, periodic with a short or very long period, very near periodic, or completely aperiodic or chaotic. Hence, it is possible to enhance heat transfer while maintaining safety in two-phase flow systems by operating them in an oscillatory mode.
- Research Organization:
- Univ. of Virginia, Dept. of Nuclear Engineering and Engineering Physics, Charlottesville, VA (US)
- OSTI ID:
- 6050845
- Journal Information:
- Nucl. Sci. Eng.; (United States), Vol. 100:4
- Country of Publication:
- United States
- Language:
- English
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