Liquid holdup measurement of permittivity-changing gas-liquid two-phase flow by multimode microwave resonant cavity

The accurate measurement of gas–liquid two-phase flow has been a key issue in multiple engineering fields but remains challenging. During the long-term monitoring of the liquid holdup in gas–liquid two-phase flow, the permittivity of the flow may change frequently due to inevitable environmental fluctuations, and the measurement errors can accumulate and become significant. In this work, a multimode resonant cavity based on the perturbation method is developed to achieve the accurate measurement of liquid holdup in long-term monitoring despite permittivity changes. The detailed design process, focusing on sensitivity optimization and waveguide characterization, is described. By simultaneously considering the resonant frequency and quality factor under multiple resonant modes, a compensation method for holdup measurement is proposed that adaptively mitigates the adverse impact of property changes without the need of frequent calibrations. Experiments covering the full holdup range are conducted using white oil and air. By mixing #68 white oil with #10 white oil in different ratios, the permittivity changes of the liquid phase are simulated. Results show that the full-range measurement errors are less than 0.8% with the permittivity unchanged, with a rooted mean standard error (RMSE) of 0.31%. When the permittivity of the liquid change by up to 3.18%, the errors are reduced from up to 9.84% to less than 2.05%, with an RMSE of 0.67%, by applying the compensation method. This manifests that the proposed method can effectively mitigate cumulative measurement errors induced by environmental changes, making it viable for long-term monitoring without frequent off-line calibrations.