Detecting unstable periodic orbits from oil-gas-water three-phase slug flows

We use the close return method combined with adaptive threshold selection to detect the unstable periodic orbits from the signals measured from experimental oil-gas-water three-phase slug flows, and find that the period of the emulsion type slug flow is longer than that of oil in water type slug flow. Especially, the orbit of oil in water type slug flow is basically composed of one big loop and one small loop, and the emulsion type slug flow orbit is composed of two big smooth loops. In addition, we employ the method of adaptive optimal kernel time-frequency representation to investigate the flow behaviors of two typical oil-gas-water three-phase slug flows and indicate that the energy of the oil in water slug flow exhibits a dispersed distribution and its frequency spectrum consists of various components distributes in a wide range. In contrast, the energy of emulsion type slug flow is distributed in a rather concentrated region and the high frequency component in its frequency spectrum is much less than that of the oil in water slug flow. These results are well consistent with the detected structure of unstable periodic orbit, further suggesting that the fluid mechanism underlying oil in water type slug flow is more complicated than that of the emulsion type slug flow.