Mathematical model and numerical study of internal flow of vortex grippers varying chamber eccentricity and inlet configuration to optimize suction force

Vortex grippers enable non-contact handling through confined swirling flow, yet predictive models remain limited for non-circular chambers and low-pressure operation. This work develops a generalized analytical model for circular and elliptical vortex chambers parameterized by inlet velocity. The formulation advances previous circular-chamber models by replacing the solid-body assumption with a power-law tangential-velocity profile, introducing a pneumatic-efficiency correction linking inlet and effective wall speeds, and extending the framework to elliptical chambers. The methodology combines literature-based benchmarking of circular chambers from Wang et al. with three-dimensional steady RANS CFD simulations in ANSYS Fluent for eight new geometries with one or two inlets, top or bottom placement, and inlet velocities of 35 and 50 m/s. For the Wang benchmark cases (D = 34 and 44 mm), maximum-force deviations remain below 0.7% for CFD and 1.2% for the analytical model. For the new configurations, circular two-inlet cases yield F_Base/F_Pred=0.78–1.07, whereas elliptical two-inlet cases yield 0.64–0.86; in all cases, the external peak suction exceeds the in-chamber analytical prediction by factors of 1.24–2.75. Circular chambers provide the largest suction forces, whereas elliptical chambers extend the low-pressure footprint along the major axis, which is advantageous for elongated delicate objects. Overall, the results support rapid design-oriented screening, clarify the trade-off between maximum suction force and footprint extension, and indicate that effective vortex-gripper operation is feasible in a low-pressure regime representative of compact electric blowers.