MULTI-FRACTAL ANALYSIS OF CHAOTIC FLASHING-INDUCED INSTABILITIES

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

NUCLEAR REACTOR THERMAL HYDRAULICS. INTERNATIONAL MEETING. 12TH 2007. (5 VOLS) NURETH 12

American Nuclear Society

Lugar: Pittsburgh, Pennsylvania; Año: 2007; p. 853 - 870

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). Forgiven temperatures at the inlet of the heated channels, the dynamics of the flow oscillationsexhibits an a-periocal behaviour, which is attributed to deterministic chaos. This is proven byperforming a Continuous Wavelet Transform of the measured time series of the primary flowrate. Any hidden self-similarity in the measurement is seen in the corresponding scale-spaceplane. The novelty of the present investigation lies within the multi-fractal approach used forcharacterizing the chaos. Both non-linear time series analysis (Higuchi’s method and DetrendedFluctuation Analysis) and wavelet-based analysis (Wavelet-Transform Modulus-Maxima)methods show that the dynamics of the flow oscillations has a multi-fractal structure. The strangeattractor corresponding to the dynamics of the system can thus be described as a set ofinterwoven mono-fractal objects. The global singular properties of the measured time series isthen fully characterized by a spectrum of singularities ( ) f α , which is the Hausdorff dimensionof the set of points where the multi-fractal object has singularities of strength (or Hölderexponents of) α. Whereas Higuchi’s method and Detrended Fluctuation Analysis allow easilydetermining 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 fractalspectrum.