MULTI-FRACTAL ANALYSIS OF CHAOTIC FLASHING-INDUCED INSTABILITIES

DEMAZIÈRE C.; MARCEL CHRISTIAN PABLO; ROHDE, M.; VAN DER HAGEN, T.H.J.J.

Sheraton Station Square, Pittsburgh, Pennsylvania, EEUU

Conferencia; 12th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-12); 2007

American Nuclear Society

In this paper, two-phase flow oscillations at the low pressure, low power, natural circulationCIRCUS test facility (Delft University of Technology) are investigated in a two-riserconfiguration. 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 α , which is the Hausdorff dimension of the set of points where the multi-fractal object has singularities of strength (or Hölder exponents of) α. 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.