Spatio-temporal complexities and chaos in a two-phase flashing flow

In order to study the two-phase natural circulation phenomena in a hot-leg-U-bend, an important aspect of a small-break loss-of-coolant accident in a light-water reactor, a Freon-113 flow visualization loop for simulating the natural circulation flow and various effects that occur in the process has been constructed based on the predetermined scaling criteria. Since the void fraction distribution represents the major factor in determination of flow rate, interruption and re-establishment of the two-phase natural circulation, we present a space-time description of regular and complex phenomena based on the bi-orthogonal decomposition of a spatio-temporal void fraction distribution into orthogonal temporal modes (chronos) and orthogonal spatial modes (topos) (Aubry, 1991). Such a description allowed for the computation of global (spatial and temporal) quantities such as the energy of the void fraction configuration, global entropy and characteristic dimension (the effective number of degrees of freedom of the signal). The global energy function is used to identify the space-time structures independently participating in the (kinetic) energy of the flow. The global entropy characterizes the full space and time structure of the signal and we use this quantity to obtain an objective indicator of different flow regimes appearing in two-phase natural circulation flow.