Spectral Characterization of Hydrodynamic Regimes in Multiphase Mixing Using PSD Analysis and CFD Simulations

The performance of gas–liquid–solid coaxial mixing systems is controlled by a complex interplay between liquid circulation, gas distribution, particle transport, and unsteady flow phenomena generated by the interacting impellers. Traditional design and evaluation parameters, such as power draw, provide a measure of the energy supplied to the system but offer limited information regarding the manner which this energy is transferred across different hydrodynamic structures and mixing mechanisms. To address this limitation, the present work investigates the behavior of a three-phase coaxial mixer containing a shear-thinning CMC solution combining experimental measurements with CFD simulations. Gas holdup and solids distribution were quantified using pressure measurements and electrical resistance tomography, while torque fluctuations from the two impellers were analyzed in the frequency domain through power spectral density (PSD) techniques. To interpret the spectral characteristics of the system, a frequency-based assessment methodology was established using three complementary indicators. The Spectral-Entropy Stability Index (SI) was introduced to evaluate the degree of spectral concentration within each impeller response, the Spectral Cooperation Ratio (SCR) was employed to characterize dynamic coupling between the impellers, and the Stability–Efficiency Gap was defined to assess how effectively spectral organization contributes to cooperative mixing behavior. Analysis of the results revealed that upward-pumping operation produced more effective particle suspension by maintaining greater dynamical separation between the anchor and central impellers, whereas downward-pumping operation favored gas retention and dispersion through increased frequency-domain synchronization. Mapping the operating conditions within an SI–SCR framework enabled the identification of distinct hydrodynamic regimes associated with enhanced solids suspension and improved gas dispersion. Numerical simulations also provided additional mechanistic insight into the flow structures underlying the observed spectral behaviour, revealing that similar spectral responses may originate from fundamentally different hydrodynamic phenomena.