Flow-induced acoustic source analysis in a semi-axial multistage pump: Scaling with operating conditions and efficiency

Unsteady flow in hydraulic turbomachinery generates hydrodynamic pressure fluctuations that are relevant both to acoustic emissions and to the structural excitation of the machine. How hydraulic efficiency, off-design flow topology and fluid-induced source mechanisms relate remains incompletely characterized, yet is central to pump design and operation. This work investigates the fluid-side source mechanisms in a semi-axial multistage pump through unsteady Reynolds-Averaged Navier–Stokes simulations at two rotational speeds (50 Hz and 75 Hz) spanning twelve operating points. Fluid-induced source terms are extracted using two complementary formulations: Lighthill’s quadrupole term and the Perturbed Compressible Equations (PCE). A new volume-averaged metric, the Average Volume Noise (AVN), is introduced to quantify the intensity of the hydrodynamic acoustic-source field. Results show that source intensity exhibits a distinct minimum at the best efficiency point and increases asymmetrically off-design: at high flow coefficients, AVN rises sharply due to stator separation and vortex shedding; at low flow coefficients, the increase is milder, dominated by rotor recirculation. When non-dimensionalized, AVN curves for both speeds collapse onto a single trend versus a non-dimensionalized discharge (ϕ), indicating that flow-induced source intensity scales with the same similarity parameter governing hydraulic performance. These findings provide a physically grounded framework for relating operating condition, flow topology and fluid-side source strength in semi-axial turbomachinery, relevant to subsequent vibro-acoustic and fluid-structure-interaction analyses.