Low-order modelling of a leading-edge vortex growing from a feeding sheet

Recent advances in the unsteady potential-flow model have shown promise in providing a low-order theoretical framework for studying insect aerodynamics. Although the assimilation of the discrete-vortex method enables accurate predictions of unsteady aerodynamic forces and wake structure evolution, it remains physically meaningful to seek a minimal representation of the coherent vortices while retaining the essential dynamical coupling between the concentrated vortex core, the feeding shear layer and the wing. The present study explores various reduction strategies in modelling the growth of a leading-edge vortex (LEV) on an accelerating flat plate. The results argue against the use of a single free point vortex, as it completely fails to capture the dynamical effect of vorticity feeding from the wing to the vortex core. By incorporating the momentum conservation of the vorticity-feeding process, both the classical Brown–Michael and the vortex-merge approaches provide notable improvements in predicting lift and wake vortex dynamics. The performance can be further improved by introducing an array of discrete vortices to account for the vorticity-feeding sheet. In particular, a new vortex-merge scheme is proposed to physically determine the vorticity transfer from the feeding sheet to the concentrated vortex core, based on the local rotation strength of the sheet. This yields satisfactory performance in capturing the lift variation, LEV advection and circulation growth rate. Crucially, the proposed physical-merge concept underscores a key insight for low-order modelling of a wing-attached vortex with varying strength: sufficient fidelity is required in resolving both the feeding shear layer and low-rotation vortical structure.