Multi-fractal analysis of chaotic flashing-induced instabilities

Paper in proceeding, 2007

In this paper, two-phase flow oscillations at the low pressure, low power, natural circulation CIRCUS test facility (Delft University of Technology) are investigated in a two-riser configuration. These oscillations are driven by flashing (and to some extent by geysering). For given temperatures at the inlet of the heated channels, the dynamics of the flow oscillations exhibits an a-periocal behaviour, which is attributed to deterministic chaos. This is proven by performing a Continuous Wavelet Transform of the measured time series of the primary flow rate. Any hidden self-similarity in the measurement is seen in the corresponding scale-space plane. The novelty of the present investigation lies within the multi-fractal approach used for characterizing the chaos. Both non-linear time series analysis (Higuchi’s method and Detrended Fluctuation Analysis) and wavelet-based analysis (Wavelet-Transform Modulus-Maxima) methods show that the dynamics of the flow oscillations has a multi-fractal structure. 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.