Multi-fractal analysis of chaotic flashing-induced instabilities in boiling channels in the natural circulation CIRCUS facility

Artikel i vetenskaplig tidskrift, 2008

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 an erratic behaviour. This study demonstrates that this behaviour 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 multi-fractal approach used for characterizing the chaos. Both non-linear time series analysis and wavelet-based analysis methods show that the dynamics of the flow oscillations has a multi-fractal structure. For the former, both Higuchi’s method and Detrended Fluctuation Analysis 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 a set of interwoven mono-fractal objects. The global singular properties of the measured time series is then fully characterized by a spectrum of singularities f(alpha), which is the Hausdorff dimension of the set of points where the multi-fractal object has singularities of strength (or Hölder exponents of) alpha. Whereas Higuchi’s method and Detrended Fluctuation Analysis allow easily determining whether the deterministic chaos has a mono- or multi-fractal hierarchy, the Wavelet-Transform Modulus-Maxima has the advantage of giving a quantitative estimation of the fractal spectrum. The time-modelling of such a behaviour of the facility is therefore difficult since there is sensitive dependence on initial conditions. From a regulatory point-of-view, such a behaviour of natural circulation systems in a multiple riser configuration has thus to be avoided.