Tracking-free topological measurement in vertical gas-liquid pipe flow: calibration, precision, and selectivity

Video tracking cannot follow the large gas structures of slug, churn and annular flow: they overlap in projection, and they merge and split continually. We instead read the rate of change of the Euler Characteristic Surface - the difference between the numbers of connected gas and liquid regions in a thresholded frame, across morphological scales - and characterize it as an instrument before reading physics from it, on 1.4 hours of flow filmed in slow motion at 240 Hz in 2-inch and 1-inch vertical air-water pipes. It is not an event count: a surrogate preserving only the count's distribution and power spectrum reproduces 94% of it in the 2-inch pipe (75% in the 1-inch), so it measures how widely and how quickly the count of large structures varies, and its value depends on the persistence window of its filter. Against conductance probes on an independent facility filming at 800 Hz, an image-derived structure arrival rate agrees to 7.2%, and replicate filming bounds single-series precision at 29% (13% at mid-station). So qualified, activity falls with gas velocity in the 2-inch pipe through the amplitude of the count's fluctuations. The two pipes differ at matched Froude number, but the rate grows with the area analysed, which was not controlled, so no diameter effect is established. To our knowledge this is the first calibration of a topological descriptor's rate of change against an independent instrument, with an explicit null model and a stated noise floor.