On the detection of a low-dimensional attractor in disperse two-component (oil-water) flow in a vertical pipe

Abstract The flow of multiphase and multicomponent mixtures in pipes is one of the greatest unsolved problems of modern process engineering. The complexity of the behaviour has meant that all but the simplest phenomena have remained unexplored, both experimentally and theoretically. The droplet flow regime in an oil-water flow in a vertical pipe is investigated by using impedance and ultrasonic techniques. The data are analysed with the Grassberger-Procaccia algorithm. The dimension of the attractor governing the flow is found to be the same ( D ≈ 5) within experimental error for both methods. Limitations to the technique are described and the concept of a flow regime map derived in terms of attractor dimension (fractal or Hausdorf-Besicovich) contours is presented.