Hysteretic tip-leakage vortex dynamics in a variable-speed multiphase pump

Abstract

A pronounced hysteretic response is identified between imposed rotational-speed variation and rigid-vorticity evolution in a tip-leakage vortex (TLV). Identical rotational speeds during acceleration and deceleration correspond to different vortex intensities and spatial configurations, revealing a memory effect in the internal rotating flow. This behavior is investigated in a gas–liquid rotodynamic multiphase pump using transient numerical simulation, Liutex–Omega vortex identification, rigid-vorticity decomposition, and transport analysis. The hysteresis arises from a mismatch between the timescale of external speed forcing and the relaxation timescale of the vortical flow. After the rotational speed changes, the preexisting vortex system undergoes viscous attenuation and structural reorganization before establishing a configuration compatible with the new operating condition. During acceleration, inherited vortex structures initially weaken and then develop into a stronger, more concentrated vortex system. During deceleration, fluid inertia temporarily sustains the leakage-jet momentum and previously established vortices, delaying their attenuation and breakdown. The Coriolis-related rotational term and the rigid-vorticity viscous-diffusion term dominate this transient response, while the pseudo-Lamb term promotes rigid-vorticity quasi-generation during acceleration. Stretching and dilatation mainly regulate localized vortex-tube deformation and make smaller overall contributions. These results show that TLV evolution under transient forcing is controlled by relaxation, reorganization, and flow memory rather than responding instantaneously or monotonically to rotational speed, providing a generalizable description of hysteretic vortex dynamics in variable-speed rotating flows.