Unsteady Air Concentration and Velocity Estimation with Conductivity Probes for Wave Run-up Applications

Air-water flows are present in some of the most challenging hydraulic engineering and coastal applications. At large scales, high velocities and associated levels of turbulence lead to air entrainment, which manifests as a multiphase flow consisting of bubbles and droplets, travelling dispersed in the reciprocal phase together with more complex flow structures. Given the intrinsic handicap of air-water flows for common single-phase instrumentation, most relevant experimental insights have come through the use of phase detection probes, such as conductivity or optical fibre probes. These probes are based on a synchronized double recording of phase fraction signals at two tips separated by a known distance. For steady flows, both signals can be cross-correlated to obtain the most probable lag time and hence estimate the mean interfacial velocity. However, when flows are unsteady, holding short characteristic times, a long time series cross-correlation is not feasible anymore. Seeking for a robust analysis methodology, collaborative experimental tests have been conducted in the wave flume “Schneiderberg” at the Ludwig-Franzius-Institute in Hannover, Germany. In this study, several groups of regular waves, with different wave heights and periods, have been generated and the run-up process over a stepped revetment has been studied using a conductivity probe, placed at several locations around the still water level. A novel data analysis, namely adaptive window cross-correlation, has been applied to the recorded signals, disclosing characteristic air concentration levels and pseudo-instantaneous interfacial velocities. Additional insight has been gained through the use of a high-speed camera, confirming the main findings of the adaptive cross-correlation technique. Relevant discussion on experimental possibilities for future analysis of air-water flows in coastal applications is presented in this study.