Numerical Evaluation and Assessment of Key Two-Phase Flow Parameters Using Four-Sensor Probes in Bubbly Flow

Intrusive phase-detection probes remain a standard tool for local characterization of gas-liquid bubbly flows, but their accuracy is strongly affected by probe geometry and bubble-probe interaction kinematics. This work presents a Monte Carlo-based framework to evaluate four-sensor intrusive probes in bubbly flow, relaxing the classical assumptions of spherical bubbles and purely axial trajectories. Bubbles are represented as spheres or ellipsoids, a broad range of non-dimensional probe geometries are explored, and local quantities such as interfacial area concentration, bubble and flux velocities, and chord lengths are recovered from synthetic four-sensor signals. The purpose of the framework is threefold: (i) it treats four-sensor probes in a unified way for interfacial area, velocity, and chord length estimation; (ii) it includes ellipsoidal bubbles and statistically distributed incidence angles; and (iii) it yields compact correction laws and design maps expressed in terms of the spacing-to-diameter ratio ap/D, the dimensionless probe radius rp/D, and the missing ratio mr (defined as the fraction of bubbles that cross the probe footprint without being detected), which can be applied to different intrusive four-sensor probes. The numerical results show that, within a recommended geometric range 0.5≤ap/D≤2 and rp/D≤0.25 and for missing ratios mr≤0.7, the axial velocity Vz estimates the bubble centroid velocity and its projection with typical errors within ±10%, while a chord length correction CLcorr(mr) recovers the underlying chord length distribution with a residual bias of only a few percent. The proposed interfacial area correction, written solely in terms of mr, remains accurate in polydisperse bubbly flows. Outside the recommended (ap/D,rp/D) range, large probe radius or extreme tip spacing lead to velocity and chord length errors that can exceed 20-30%. Overall, the framework provides quantitative guidelines for designing and using four-sensor intrusive probes in bubbly flows and for interpreting their measurements through geometry-aware correction factors.