An improved CFD-based correlation for ultrasonic Doppler flowmeter measurement of oil-water two-phase flow

Accurate oil–water flow measurement is critical for safe operation and economic efficiency, particularly for properly managing oil and water handling in industrial systems. However, the complex and asymmetric structure of oil–water flow makes accurate velocity measurement highly challenging, requiring sometimes intrusive, advanced instrumentation involving difficult calibration. Continuous Wave Doppler Ultrasound (CWDU) flowmeters offer a non-invasive, clamp on alternative for measuring oil–water two phase flow, but their accuracy depends on reliable correlations to convert local velocity readings into a cross sectional mean velocity. This study proposes an improved physics-based model for CWDU flowmeters, developed using three-dimensional CFD simulations of oil–water flow validated against experimental data. The investigated flow conditions covered Reynolds numbers from approximately 1,100 to 60,000, spanning transitional and fully turbulent regimes. A steady state SST k-ω turbulence model was employed because it provides reliable accuracy for oil–water two phase flow. The model integrates CFD-generated local velocity and phase fraction profiles with CWDU measurements to improve prediction accuracy. Velocity profiles were approximated using a power-law distribution, while phase fraction exhibited wall-peaked characteristics. CFD provides full radial velocity profiles, while the CWDU records only local mean velocities. To relate these measurements, the CWDU-recorded local velocities were numerically integrated in reverse to identify their corresponding radial positions, enabling extraction of equivalent local mean velocities from the CFD profiles. These estimates were applied to scale and correct CWDU readings, establishing a CFD-based correlation for overall mean velocity. This approach reduced average error from 9.9% to 6.1% compared to theoretical correlations. Furthermore, a drift-flux model was employed to predict oil and water superficial velocities from the corrected mean velocity, achieving high accuracy with average percentage errors of 0.57% for oil and –3.74% for water, and standard deviations of 9.9% and 10.9%, respectively. The integration of CWDU flowmeters with CFD-derived velocity distributions significantly enhances measurement reliability for oil–water systems, supporting industrial deployment. Flow profile exponents were further used to create a dynamic distribution parameter for the drift-flux model, proving effective for estimating phase-specific superficial velocities.