Power spectral density analysis of torque fluctuations and hydrodynamic characterization of co-rotating gas–solid–liquid coaxial mixers

The hydrodynamic behavior of a gas–liquid–solid coaxial mixer is governed by complex interactions among impeller-generated circulation, gas dispersion, particle suspension, and flow instabilities. Conventional indicators such as power consumption quantify overall energy input but provide limited insight into how energy is distributed among underlying flow structures. This study investigates the effects of central impeller speed, anchor speed, gas flow rate, and pumping direction on the performance of a three-phase coaxial mixer containing a non-Newtonian CMC solution using combined experimental and numerical approaches. Solid suspension and gas holdup were measured using tomography and pressure measurements, while torque signals from both impellers were analyzed through power spectral density analysis over 96 operating conditions. A spectral framework comprising the Spectral-Entropy Stability Index, Spectral Cooperation Ratio, and Stability–Efficiency Gap was developed to quantify spectral order, inter-impeller coupling, and the extent to which spectral stability translates into cooperative performance. Results highlight the importance of combining spectral stability and spectral cooperation metrics to accurately characterize mixing performance. Upward pumping promoted superior solid suspension through greater spectral independence of the anchor impeller, whereas downward pumping enhanced gas dispersion through stronger inter-impeller entrainment. The proposed operating-zone framework identified ordered-independent and dynamic-entrained regimes as the most favorable states for solid suspension and gas dispersion, respectively. CFD simulations, validated against torque and holdup measurements within 5–19.25%, showed that similar spectral signatures can originate from different hydrodynamic mechanisms. The combined PSD–CFD methodology provides a practical framework for identifying hydrodynamic regimes and optimizing multiphase coaxial mixing operations.