Multifractal Analysis of Chaotic Flashing-Induced Instabilities in Boiling Channels in the Natural-Circulation CIRCUS Facility

摘要

In this paper, two-phase-flow oscillations at the natural-circulation CIRCUS test facility are investigated in a two-riser configuration. These oscillations are driven by flashing (and to some extent by geysering). For a given range of operating conditions of the facility, the oscillations exhibit erratic behavior. This study demonstrates that this behavior can be attributed to deterministic chaos. This is proven by performing a continuous wavelet transform of the measured time series. Any hidden self-similarity in the measurement is seen in the corresponding scale-space plane. The novelty of the present investigation lies with the multifractal approach used for characterizing the chaos. Both nonlinear time series analysis and wavelet-based analysis methods show that the dynamics of the flow oscillations has a multifractal structure. For the former, both Higuchi's method and detrended fluctuation analysis (DFA) were used, whereas for the latter, the wavelet-transform modulus-maxima method was used. The strange attractor corresponding to the dynamics of the system can thus be described as α set of interwoven monofractal objects. The global singular properties of the measured time series is then fully characterized by a spectrum of singularities f (α), which is the Hausdorff dimension of the set of points where the multifractal object has singularities of strength (or Holder exponents of) α. Whereas Higuchi's method and DFA allow easily determining whether the deterministic chaos has a monofractal or multifractal hierarchy, the wavelet-transform modulus-maxima has the advantage of giving α quantitative estimation of the fractal spectrum. The time-modeling of such behavior of the facility is therefore difficult since there is sensitive dependence on initial conditions. From a regulatory point of view, such behavior of natural-circulation systems in a multiple-riser configuration has thus to be avoided.