Small amplitude kinematic wave propagation in two-component media

Abstract

Experimentally determined attenuation and propagation characteristics are presented for small amplitude concentration waves in vertical bubbly and particulate flows. These were studied up to concentrations of 44.3 and 58%, respectively, in a 10 cm pipe. The wave propagation was studied in terms of the time delay, phase lag and loss of coherence of naturally occurring volume fraction fluctuations by means of simultaneous impedance measurements at two separate locations. Small amplitude natural kinematic waves were confirmed to be non-dispersive, as has previously been shown by other investigators. In this system configuration, bubbly flows undergo a regime transition to churn-turbulence, and not to slug flows as is typically observed in smaller diameter pipes. A dramatic drop in the attenuation time constant of small kinematic waves was found prior to the transition to churn-turbulence in gas-liquid flows, indicating that the regime change is the consequence of a loss of kinematic stability. The solid-liquid mixtures studied were found to always remain stable, with a range of greatest stability between 15–20%, as indicated by a maximum in the kinematic wave attenuation constant. The idea of a stable intermediate range of concentrations is consistent with the observations by Homsy et al. [Int. J. Multiphase Flow 6, 305–318 (1980)], who first observed structure formation above and below such a range. At concentrations above 40%, gradual transition to plug flow occurs, in which the particles execute little or no motion relative to one another.