A triple source model of pressure fluctuation analysis for a mixed-flow pump

This paper investigates the physical origins of pressure fluctuations on the stationary shroud wall of a mixed-flow pump. A novel ‘triple source model’ is developed and applied to experimental validated stress-blended eddy simulations. The model decomposes stationary-frame pressure fluctuations into three distinct rotating-frame components to disentangle complex tip leakage vortex (TLV) interactions: (i) kinematic ‘non-uniform fluctuation’ ( $p_{\textit{NUF}}$ ) from the steady blade sweep, (ii) dynamic ‘flow synchronous fluctuation’ ( $p_{\textit{FSF}}$ ) phase-locked to rotation, and (iii) ‘flow asynchronous fluctuation’ ( $p_{\textit{FAF}}$ ) from all non-phase-locked phenomena. Analysis reveals that shroud unsteadiness is over 90 % dominated by the synchronous components along the TLV trajectory. Crucially, the model uncovers a counter-intuitive destructive interference mechanism between the kinematic sweep $p_{\textit{NUF}}$ and the dynamic response $p_{\textit{FSF}}$ , with local cross-correlation coefficient –0.26, explaining how dynamic instabilities can dampen the steady pressure footprint. Source-term analysis of the pressure Poisson equation establishes a complete causal chain from specific velocity field interactions to pressure signatures: (i) the non-uniform fluctuation is kinematically driven by the mean momentum flux from blade loading, contributing 52.27 % to the local pressure asymmetry; (ii) the flow synchronous fluctuation is generated by periodic vortex–turbulence interaction, contributing 80.22 % of its total source; (iii) and the asynchronous broadband pressure is sourced from the canonical turbulent cascade, contributing 79.33 % of its total source. Spatial correlations confirm the TLV as the common physical nexus for all components. This work establishes a quantitative diagnostic framework that moves beyond qualitative vortex observation, providing a physical basis for the targeted mitigation of turbomachinery unsteadiness.